The variation of the uncentered maximal operator with respect to cubes

Authors: Julian Weigt

Source: Journal of the European Mathematical Society. 27:2531-2570

Subject Terms: Mathematics - Analysis of PDEs, maximal function, Maximal functions, Littlewood-Paley theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, variation, 0101 mathematics, 42B25, 26B30, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2109.10747
https://zbmath.org/8030710
https://doi.org/10.4171/jems/1575

BV Functions and Nonlocal Functionals in Metric Measure Spaces: BV functions and nonlocal functionals in metric measure spaces

Authors: Lahti P., Pinamonti A., Zhou X.

Source: The Journal of Geometric Analysis. 34

Subject Terms: nonlocal functional, function of bounded variation, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, Functional Analysis (math.FA), Mathematics - Functional Analysis, 46E36, 26B30, Sobolev (and similar kinds of) spaces of functions on metric spaces, analysis on metric spaces, metric measure space, Sobolev function, Poincaré inequality, FOS: Mathematics, 26B30, 46E36, Function of bounded variation, Metric measure space, Nonlocal functional, Poincaré inequality, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.08882
https://hdl.handle.net/11572/438271
https://doi.org/10.1007/s12220-024-01766-8

Alberti's rank one theorem and quasiconformal mappings in metric measure spaces

Authors: Panu Lahti

Source: Journal of Functional Analysis. 288:110758

Subject Terms: Analysis on metric spaces, Mathematics - Metric Geometry, Quasiconformal mappings in metric spaces, FOS: Mathematics, quasiconformal mapping, Ahlfors regular metric measure space, Alberti's rank one theorem, Metric Geometry (math.MG), 30L99, 30L10, 26B30, 0101 mathematics, function of bounded variation, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation

File Description: application/xml

Access URL: http://arxiv.org/abs/2303.09157
https://zbmath.org/7962979
https://doi.org/10.1016/j.jfa.2024.110758

Relaxation of certain integral functionals depending on strain and chemical composition

Authors: Ana Margarida Ribeiro, ZAPPALE, ELVIRA

Source: Chinese Annals of Mathematics, Series B. 34:491-514

Subject Terms: quasiconvexity, Mathematics - Analysis of PDEs, relaxation, Methods involving semicontinuity and convergence, functions of bounded variation, Coupling of solid mechanics with other effects, FOS: Mathematics, Relaxation, Convexity of real functions of several variables, generalizations, Absolutely continuous real functions of several variables, functions of bounded variation, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/pdf/1211.2574
http://arxiv.org/abs/1211.2574
https://www.iris.unisa.it/handle/11386/3878695
https://link.springer.com/article/10.1007/s11401-013-0784-x
https://hdl.handle.net/11386/3878695
https://doi.org/10.1007/s11401-013-0784-x

Regular Carathéodory-type selectors under no convexity assumptions

Authors: Vyacheslav V. Chistyakov, A. Nowak

Source: Journal of Functional Analysis. 225:247-262

Subject Terms: MAPPINGS, Functions of bounded variation, generalizations, Carathéodory multifunction, metric semigroup, MEASURABLE SELECTIONS, Set-valued functions, 01 natural sciences, Metric semigroup, Absolutely continuous real functions of several variables, functions of bounded variation, compact values, Bounded variation, MAPS, bounded variation, Compact values, absolute continuity, BOUNDED VARIATION, Selector, Selections in general topology, Lipschitz multifunction, Set-valued set functions and measures, integration of set-valued functions, measurable selections, 0101 mathematics, Analysis, Caratheodory multifunction, Set-valued maps in general topology, selector

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https://doi.org/10.1016/j.jfa.2005.03.024
https://research.rug.nl/en/publications/ac9ee4e5-f802-4209-9961-4066c9e422d7
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https://www.rug.nl/research/portal/publications/regular-caratheodorytype-selectors-under-no-convexity-assumptions(ac9ee4e5-f802-4209-9961-4066c9e422d7)/export.html
https://www.sciencedirect.com/science/article/pii/S0022123605001540
https://research.rug.nl/en/publications/regular-caratheodory-type-selectors-under-no-convexity-assumption
https://core.ac.uk/display/82096653
https://publications.hse.ru/mirror/pubs/share/folder/0r0i4d74bm/direct/75256858

A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. I: A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. II

Authors: Vyacheslav V. Chistyakov

Source: Nonlinear Analysis: Theory, Methods & Applications. 62:559-578

Subject Terms: MAPPINGS, finite total variation, SUBSTITUTION, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, Representation and superposition of functions, Banach algebras of continuous functions, function algebras, COMPOSING FUNCTIONS, Banach algebra property, PRINCIPLE, superposition operator, Lipschitz condition, 0101 mathematics, functions of several variables

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https://www.narcis.nl/publication/RecordID/oai%3Apure.rug.nl%3Apublications%2Fda5f6038-147e-40c1-aa00-61005fca192a
https://research.rug.nl/en/publications/a-banach-algebra-of-functions-of-several-variables-of-finite-tota-2
https://www.rug.nl/research/portal/en/publications/a-banach-algebra-of-functions-of-several-variables-of-finite-total-variation-and-lipschitzian-superposition-operators-i(be411485-8797-4bbb-a86d-2aa793b8557b).html
https://www.sciencedirect.com/science/article/pii/S0362546X05004001
https://core.ac.uk/display/92452927

Optimal lifting for BV(S 1,S 1): Optimal lifting for BV \(( S^{1}, S^{1})\)

Authors: Radu Ignat

Source: Calculus of Variations and Partial Differential Equations. 23:83-96

Subject Terms: optimal lifting, Banach algebras of continuous functions, function algebras, functions of bounded variation, Variational problems in a geometric measure-theoretic setting, 0101 mathematics, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation

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Access URL: https://link.springer.com/content/pdf/10.1007/s00526-004-0291-8.pdf
https://link.springer.com/article/10.1007/s00526-004-0291-8

Integration over the levels of ACL-functions

Authors: B. P. Kufarev, N. G. Nikulina

Source: Mathematical Notes. 77:499-502

Subject Terms: absolutely continuous functions, repeated integration, Sobolev class, multidimensional variations, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences, Hausdorff measure, Absolutely continuous real functions of several variables, functions of bounded variation

File Description: application/xml

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https://doi.org/10.1007/s11006-005-0049-4
https://link.springer.com/article/10.1007/s11006-005-0049-4
https://link.springer.com/content/pdf/10.1007/s11006-005-0049-4.pdf

Mumford–Shah-type functionals associated with doubling metric measures: Mumford-Shah-type functionals associated with doubling metric measures

Authors: BALDI, ANNALISA, FRANCHI, BRUNO

Source: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 135:1-23

Subject Terms: Variational methods applied to PDEs, STRONG $A_{INFTY}$-WEIGHTS, MUMFORD-SHAH FUNCTIONALS, WEIGHTED $BV$ SPACES, Contents, measures, outer measures, capacities, 0101 mathematics, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation

File Description: application/xml

Access URL: https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/mumfordshahtype-functionals-associated-with-doubling-metric-measures/D2627FAE33F380B331A95AEE2A61F835
https://cris.unibo.it/handle/11585/681
https://hdl.handle.net/11585/681
https://doi.org/10.1017/S0308210500003735

Functions of bounded variation on compact subsets of the plane

Authors: Brenden Ashton, Ian Doust

Source: Studia Mathematica. 169:163-188

Subject Terms: absolutely continuous functions, AC-operators, well-bounded operators, functions of bounded variation, Spectral operators, decomposable operators, well-bounded operators, etc, functional calculus, 0101 mathematics, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation

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https://zbmath.org/2159584
https://doi.org/10.4064/sm169-2-5
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/169/2/90178/functions-of-bounded-variation-on-compact-subsets-of-the-plane
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https://eudml.org/doc/286381

Differentiability from the representation formula and the Sobolev–Poincaré inequality: Differentiability from the representation formula and the Sobolev--Poincaré inequality

Authors: Valentino Magnani

Source: Studia Mathematica. 168:251-272

Subject Terms: distributional derivative, Analysis on real and complex Lie groups, Inequalities involving derivatives and differential and integral operators, stratified group, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Sobolev space, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, space of functions of generalized bounded variation

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https://zbmath.org/2159571
https://doi.org/10.4064/sm168-3-5
https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/168/3/89698/differentiability-from-the-representation-formula-and-the-sobolev-8211-poincare-inequality
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http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-3-5
https://eudml.org/doc/285260

A remark on differentiable functions with partial derivatives in Lp: A remark on differentiable functions with partial derivatives in \(L^p\)

Authors: DI BARI, Cristina, VETRO, Calogero

Source: Journal of Mathematical Analysis and Applications. 299:227-234

Subject Terms: Polish group, gage, Haar null, Null set or empty set, Continuity and differentiation questions, variation, 0101 mathematics, partition, 01 natural sciences, functions of several variables, Absolutely continuous real functions of several variables, functions of bounded variation, differentiability

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/2141779
https://doi.org/10.1016/j.jmaa.2004.06.044
https://www.sciencedirect.com/science/article/pii/S0022247X04005347
https://www.sciencedirect.com/science/article/pii/S0022247X04005347#!
http://hdl.handle.net/10447/16702
https://hdl.handle.net/10447/16702
https://doi.org/10.1016/j.jmaa.2004.06.044

Convergence of double Fourier series and $W$-classes: Convergence of double Fourier series and \(W\)-classes

Authors: Mikhail Ivanovich Dyachenko, D. Waterman

Source: Transactions of the American Mathematical Society. 357:397-407

Subject Terms: Multiple Fourier series, generalized bounded variation, Fourier series and coefficients in several variables, Waterman classes, Continuity and differentiation questions, 0101 mathematics, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation

File Description: application/xml

Access URL: https://www.ams.org/tran/2005-357-01/S0002-9947-04-03525-1/S0002-9947-04-03525-1.pdf
https://www.ams.org/tran/2005-357-01/S0002-9947-04-03525-1/S0002-9947-04-03525-1.pdf
https://www.ams.org/tran/2005-357-01/S0002-9947-04-03525-1/home.html

Approximation of functions of finite variation by superpositions of a Sigmoidal function: Approximation of functions of finite variation by superpositions of a sigmoidal function.

Authors: MARINO, Giuseppe, LEWICKI G.

Source: Applied Mathematics Letters. 17:1147-1152

Subject Terms: the Lipschitz condition, Applied Mathematics, rate of approximation, Rate of approximation, The Lipschitzcondition, 01 natural sciences, Approximation by other special function classes, Absolutely continuous real functions of several variables, functions of bounded variation, sigmoidal function, Function of finite variation, Sigmoidal function, function of finite variation, Lipschitz condition, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/2140796
https://doi.org/10.1016/j.aml.2003.11.006
https://core.ac.uk/display/82426508
https://www.sciencedirect.com/science/article/pii/S089396590481694X
https://dblp.uni-trier.de/db/journals/appml/appml17.html#LewickiM04
https://www.sciencedirect.com/science/article/abs/pii/S089396590481694X
https://hdl.handle.net/20.500.11770/141176
https://ruj.uj.edu.pl/xmlui/handle/item/81694

General method of regularization. I: Functionals defined on BD space: General method of regularization. I:~Functionals defined on BD space

Authors: Jarosław L. Bojarski

Source: Applicationes Mathematicae. 31:175-199

Subject Terms: Hencky plasticity, Methods involving semicontinuity and convergence, relaxation, Regularity of solutions of equilibrium problems in solid mechanics, Optimality conditions for problems in abstract spaces, functions of bounded deformation, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials), regularization, Energy minimization in equilibrium problems in solid mechanics, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, 0101 mathematics, Set-valued operators

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/84173?download.pdf
https://eudml.org/doc/279788
https://dialnet.unirioja.es/servlet/articulo?codigo=3450543
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-4
https://www.impan.pl/shop/publication/transaction/download/product/84173?download.pdf

Local solvability of a constrainedgradient system of total variation: Local solvability of a constrained gradient system of total variation

Authors: GIGA, YOSHIKAZU, KASHIMA, YOHEI, YAMAZAKI, NORIAKI

Source: Abstract and Applied Analysis, Vol 2004, Iss 8, Pp 651-682 (2004)
Abstr. Appl. Anal. 2004, no. 8 (2004), 651-682

Subject Terms: \(p\)-harmonic map flow, 35K90, 58E20, subdifferential, Equations in function spaces, evolution equations, Degenerate parabolic equations, PDEs with multivalued right-hand sides, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, gradient flow, 35R70, total variation flow, QA1-939, Harmonic maps, etc, 0101 mathematics, 26A45, Mathematics

File Description: application/xml; application/pdf

Access URL: http://downloads.hindawi.com/journals/aaa/2004/434316.pdf
https://zbmath.org/2163681
https://doi.org/10.1155/s1085337504311048
https://doaj.org/article/36dd4d3990cb40d2bc9b74d7430023aa
http://downloads.hindawi.com/journals/aaa/2004/434316.pdf
https://downloads.hindawi.com/journals/aaa/2004/434316.pdf
https://ui.adsabs.harvard.edu/abs/2004AbApA2004..651G/abstract
https://projecteuclid.org/journals/abstract-and-applied-analysis/volume-2004/issue-8/Local-solvability-of-a-constrained-gradient-system-of-total-variation/10.1155/S1085337504311048.full
https://projecteuclid.org/download/pdfview_1/euclid.aaa/1095684286
https://www.hindawi.com/journals/aaa/2004/434316/
http://projecteuclid.org/euclid.aaa/1095684286

General method of regularization. II: Relaxation proposed by suquet: General method of regularization. II. Relaxation proposed by Suquet

Authors: Jarosław L. Bojarski

Source: Applicationes Mathematicae. 31:321-343

Subject Terms: Hencky plasticity, Methods involving semicontinuity and convergence, relaxation, Regularity of solutions of equilibrium problems in solid mechanics, Optimality conditions for problems in abstract spaces, integral representation, functions of bounded deformation, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials), regularization, limit analysis problem, Energy minimization in equilibrium problems in solid mechanics, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, 0101 mathematics, Set-valued operators

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/84092?download.pdf
https://zbmath.org/2120122
https://doi.org/10.4064/am31-3-7
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http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-3-7
https://eudml.org/doc/279012
https://www.impan.pl/shop/publication/transaction/download/product/84092?download.pdf

General method of regularization. III: The unilateral contact problem

Authors: Jarosław L. Bojarski

Source: Applicationes Mathematicae. 31:473-492

Subject Terms: Hencky plasticity, Methods involving semicontinuity and convergence, relaxation, 0211 other engineering and technologies, Regularity of solutions of equilibrium problems in solid mechanics, 02 engineering and technology, Optimality conditions for problems in abstract spaces, Contact in solid mechanics, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation, Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials), Signorini problem, Energy minimization in equilibrium problems in solid mechanics, soil mechanics, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, 0101 mathematics, the largest l.s.c.\ minorant less than the original functional

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/84450?download.pdf
https://zbmath.org/2120132
https://doi.org/10.4064/am31-4-8
https://www.impan.pl/shop/publication/transaction/download/product/84450?download.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=3450554
https://www.impan.pl/en/publishing-house/journals-and-series/applicationes-mathematicae/all/31/4/84450/general-method-of-regularization-iii-the-unilateral-contact-problem
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-4-8

Absolutely Continuous Functions of Several Variables and Quasiconformal Mappings: Absolutely continuous functions of several variables and quasiconformal mappings

Authors: Stanislav Hencl

Source: Zeitschrift für Analysis und ihre Anwendungen. 22:767-778

Subject Terms: Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, functions of bounded variation, absolute continuity, 0101 mathematics, quasiconformal maps, 01 natural sciences, Absolutely continuous real functions of several variables, functions of bounded variation

File Description: application/xml

Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0232-2064&vol=22&iss=4&rank=3
https://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=22&iss=4&rank=3
https://www.ems-ph.org/journals/show_pdf.php?issn=0232-2064&vol=22&iss=4&rank=3

Absolutely continuous functions of several variables and diffeomorphisms

Authors: Stanislav Hencl, Jan Malý

Source: Open Mathematics, Vol 1, Iss 4, Pp 690-705 (2003)

Subject Terms: change of variables, QA1-939, 26b30, 0101 mathematics, 01 natural sciences, Mathematics, Absolutely continuous real functions of several variables, functions of bounded variation, absolute continuity in several variables

File Description: application/xml

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http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.doi-10_2478_BF02475188
https://www.degruyter.com/view/journals/math/1/4/article-p690.xml?language=en
https://link.springer.com/article/10.2478/BF02475188
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https://link.springer.com/content/pdf/10.2478/BF02475188.pdf