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Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition.

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Title: Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition.
Authors: Giannetti, Flavia1 (AUTHOR) flavia.giannetti@unina.it, Treu, Giulia2 (AUTHOR) giulia.treu@unipd.it
Source: Calculus of Variations & Partial Differential Equations. May2026, Vol. 65 Issue 5, p1-26. 26p.
Subject Terms: *Calculus of variations, *Functionals, *Critical point theory
Abstract: We prove the local Lipschitz regularity of the minimizers of functionals of the form I (u) = ∫ Ω f (∇ u (x)) + g (x) u (x) d x u ∈ ϕ + W 0 1 , 1 (Ω) where g is bounded and ϕ satisfies the Lower Bounded Slope Condition. The function f is assumed to be convex but not uniformly convex everywhere. As a byproduct, we also prove the existence of a locally Lipschitz minimizer for a class of functionals of the type above but allowing the function f to be nonconvex. [ABSTRACT FROM AUTHOR]
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  – Url: https://dx.doi.org/doi:10.1007/s00526-026-03303-7
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  Data: Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition.
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  Data: <searchLink fieldCode="AR" term="%22Giannetti%2C+Flavia%22">Giannetti, Flavia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> flavia.giannetti@unina.it</i><br /><searchLink fieldCode="AR" term="%22Treu%2C+Giulia%22">Treu, Giulia</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> giulia.treu@unipd.it</i>
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  Data: <searchLink fieldCode="JN" term="%22Calculus+of+Variations+%26+Partial+Differential+Equations%22">Calculus of Variations & Partial Differential Equations</searchLink>. May2026, Vol. 65 Issue 5, p1-26. 26p.
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– Name: Abstract
  Label: Abstract
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  Data: We prove the local Lipschitz regularity of the minimizers of functionals of the form I (u) = ∫ Ω f (∇ u (x)) + g (x) u (x) d x u ∈ ϕ + W 0 1 , 1 (Ω) where g is bounded and ϕ satisfies the Lower Bounded Slope Condition. The function f is assumed to be convex but not uniformly convex everywhere. As a byproduct, we also prove the existence of a locally Lipschitz minimizer for a class of functionals of the type above but allowing the function f to be nonconvex. [ABSTRACT FROM AUTHOR]
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      – Type: doi
        Value: 10.1007/s00526-026-03303-7
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      – Code: eng
        Text: English
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        PageCount: 26
        StartPage: 1
    Subjects:
      – SubjectFull: Calculus of variations
        Type: general
      – SubjectFull: Functionals
        Type: general
      – SubjectFull: Critical point theory
        Type: general
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      – TitleFull: Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition.
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            NameFull: Giannetti, Flavia
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            NameFull: Treu, Giulia
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 65
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              Value: 5
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            – TitleFull: Calculus of Variations & Partial Differential Equations
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