Regularity for an anisotropic equation in the plane

Peter Lindqvist; Diego Ricciotti

doi:10.1016/j.na.2018.02.002

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Regularity for an anisotropic equation in the plane

Journal article

Open access

Peer reviewed

Regularity for an anisotropic equation in the plane

Peter Lindqvist and Diego Ricciotti

Nonlinear analysis, Vol.177, pp.628-636

12/2018

DOI: https://doi.org/10.1016/j.na.2018.02.002

Handle:

https://hdl.handle.net/20.500.12741/rep:9851

Abstract

Anisotropic problems

Regularity

Degenerate elliptic equations

We present a simple proof of the C1 regularity of p-anisotropic functions in the plane for 2≤p<∞. 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.

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Details

Title: Regularity for an anisotropic equation in the plane
Creators: Peter Lindqvist - Norwegian University of Science and Technology, Department of Mathematics, N-7491 Trondheim, Norway
Diego Ricciotti - University of Pittsburgh, Department of Mathematics, 301 Thackeray Hall, Pittsburgh, PA 15260, USA
Academic Unit: Mathematics/Statistics Department
Publisher: Elsevier Ltd
Publication Details: 12/2018
Identifiers: 99257883589601671; https://hdl.handle.net/20.500.12741/rep:9851; https://doi.org/10.1016/j.na.2018.02.002
Language: English