Local Lipschitz continuity for p,q−PDEs with explicit u−dependence

This article is dedicated to Emmanuele Di Benedetto, great mathematician, colleague, friend. In the spirit to treat a subject that in the last years attracted the interest of several mathematicians, and the attention of Emmanuele too, in this paper we give a first approach to the local Lipschitz con...

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Published inNonlinear analysis Vol. 226; p. 113066
Main Author Marcellini, Paolo
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.01.2023
Subjects
[formula omitted]growth conditions
Calculus of Variations
Elliptic equations
General growth conditions
Local Lipschitz continuity
Regularity of solutions
Calculus of Variations
Local Lipschitz continuity
p,q−growth conditions
Regularity of solutions
General growth conditions
Elliptic equations
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Abstract This article is dedicated to Emmanuele Di Benedetto, great mathematician, colleague, friend. In the spirit to treat a subject that in the last years attracted the interest of several mathematicians, and the attention of Emmanuele too, in this paper we give a first approach to the local Lipschitz continuity of weak solutions to a class of nonlinear elliptic partial differential equations in divergence form of the type ∑i=1n∂∂xiaix,u,Du=bx,u,Duunder p,q−growth assumptions. The novelties with respect to the mathematical literature on this topic are the general growth conditions and the explicit dependence of the differential equation on u, other than on its gradient Du and on the x variable.
AbstractList This article is dedicated to Emmanuele Di Benedetto, great mathematician, colleague, friend. In the spirit to treat a subject that in the last years attracted the interest of several mathematicians, and the attention of Emmanuele too, in this paper we give a first approach to the local Lipschitz continuity of weak solutions to a class of nonlinear elliptic partial differential equations in divergence form of the type ∑i=1n∂∂xiaix,u,Du=bx,u,Duunder p,q−growth assumptions. The novelties with respect to the mathematical literature on this topic are the general growth conditions and the explicit dependence of the differential equation on u, other than on its gradient Du and on the x variable.
ArticleNumber 113066
Author Marcellini, Paolo
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Keywords Calculus of Variations
Local Lipschitz continuity
p,q−growth conditions
Regularity of solutions
General growth conditions
Elliptic equations
Language English
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SSID ssj0001736
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Snippet This article is dedicated to Emmanuele Di Benedetto, great mathematician, colleague, friend. In the spirit to treat a subject that in the last years attracted...
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SubjectTerms [formula omitted]growth conditions
Calculus of Variations
Elliptic equations
General growth conditions
Local Lipschitz continuity
Regularity of solutions
Title Local Lipschitz continuity for p,q−PDEs with explicit u−dependence
URI https://dx.doi.org/10.1016/j.na.2022.113066
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