Regularity for an anisotropic equation in the plane

We present a simple proof of the $C^1$ regularity of $p$-anisotropic functions in the plane for $2\leq p<\infty$. We achieve a logarithmic modulus of continuity for the derivatives. The monotonicity (in the sense of Lebesgue) of the derivatives is used. The case with two exponents is also include...

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Bibliographic Details
Main Authors Lindqvist, Peter, Ricciotti, Diego
Format Journal Article
LanguageEnglish
Published 25.01.2018
Subjects
Mathematics - Analysis of PDEs
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Summary:We present a simple proof of the $C^1$ regularity of $p$-anisotropic functions in the plane for $2\leq p<\infty$. We achieve a logarithmic modulus of continuity for the derivatives. The monotonicity (in the sense of Lebesgue) of the derivatives is used. The case with two exponents is also included.
DOI:10.48550/arxiv.1801.08661