Limits of anisotropic and degenerate elliptic problems

Agnese Di Castro; Mayte Pérez-Llanos; José Miguel Urbano

doi:10.3934/cpaa.2012.11.1217

Article Contents

2012, Volume 11, Issue 3: 1217-1229. Doi: 10.3934/cpaa.2012.11.1217

This issue Previous Article A representational formula for variational solutions to Hamilton-Jacobi equations Next Article Dynamics of non-autonomous nonclassical diffusion equations on $R^n$

Limits of anisotropic and degenerate elliptic problems

1.
CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra
2.
Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon

Received: December 2010

Revised: February 2011

Published: May 2012

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Abstract

This paper analyzes the behavior of solutions for anisotropic problems of $(p_i)$-Laplacian type as the exponents go to infinity. We show that solutions converge uniformly to a function that solves, in the viscosity sense, a certain problem that we identify. The results are presented in a two-dimensional setting but can be extended to any dimension.

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Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 35J70, 35J92.

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