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 i...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Lindqvist, Peter, Ricciotti, Diego
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.01.2018
Subjects
Anisotropy
Derivatives
Regularity
Online AccessGet full text

Cover

More Information
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.
ISSN:2331-8422