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Superlinear free-discontinuity models: relaxation and phase-field approximation.

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Title: Superlinear free-discontinuity models: relaxation and phase-field approximation.
Authors: Conti, Sergio1 (AUTHOR), Focardi, Matteo2 (AUTHOR) matteo.focardi@unifi.it, Iurlano, Flaviana3 (AUTHOR)
Source: Calculus of Variations & Partial Differential Equations. Aug2026, Vol. 65 Issue 8, p1-58. 58p.
Subject Terms: *Calculus of variations, *Functions of bounded variation, *Variational approach (Mathematics), *Mathematical models
Abstract: In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth for large gradients and small jump amplitudes, respectively. A distinctive feature of this kind of models is that the functionals are defined on SBV functions whose jump sets may have infinite measure. Establishing general lower semicontinuity and relaxation results in this setting requires new analytical techniques. In addition, we propose a variational approximation of certain superlinear energies via phase-field models. [ABSTRACT FROM AUTHOR]
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  – Url: https://dx.doi.org/doi:10.1007/s00526-026-03394-2
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  Data: Superlinear free-discontinuity models: relaxation and phase-field approximation.
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  Data: <searchLink fieldCode="AR" term="%22Conti%2C+Sergio%22">Conti, Sergio</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Focardi%2C+Matteo%22">Focardi, Matteo</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> matteo.focardi@unifi.it</i><br /><searchLink fieldCode="AR" term="%22Iurlano%2C+Flaviana%22">Iurlano, Flaviana</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Calculus+of+Variations+%26+Partial+Differential+Equations%22">Calculus of Variations & Partial Differential Equations</searchLink>. Aug2026, Vol. 65 Issue 8, p1-58. 58p.
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  Data: In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth for large gradients and small jump amplitudes, respectively. A distinctive feature of this kind of models is that the functionals are defined on SBV functions whose jump sets may have infinite measure. Establishing general lower semicontinuity and relaxation results in this setting requires new analytical techniques. In addition, we propose a variational approximation of certain superlinear energies via phase-field models. [ABSTRACT FROM AUTHOR]
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        Value: 10.1007/s00526-026-03394-2
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      – Code: eng
        Text: English
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        PageCount: 58
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    Subjects:
      – SubjectFull: Calculus of variations
        Type: general
      – SubjectFull: Functions of bounded variation
        Type: general
      – SubjectFull: Variational approach (Mathematics)
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      – SubjectFull: Mathematical models
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      – TitleFull: Superlinear free-discontinuity models: relaxation and phase-field approximation.
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            NameFull: Conti, Sergio
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            NameFull: Focardi, Matteo
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            NameFull: Iurlano, Flaviana
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          Dates:
            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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              Value: 65
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              Value: 8
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            – TitleFull: Calculus of Variations & Partial Differential Equations
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