The obstacle problem for nonlinear elliptic equations with variable growth and L1-data

José Francisco Rodrigues; Manel Sanchón; José Miguel Urbano

doi:10.1007/s00605-008-0550-4

The obstacle problem for nonlinear elliptic equations with variable growth and L1-data

José Francisco Rodrigues, Manel Sanchón, José Miguel Urbano

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

The aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L1. © 2008 Springer-Verlag.

Original language	English (US)
Pages (from-to)	303-322
Number of pages	20
Journal	Monatshefte fur Mathematik
Volume	154
Issue number	4
DOIs	https://doi.org/10.1007/s00605-008-0550-4
State	Published - Aug 1 2008
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

General Mathematics

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abstract = "The aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L1. {\textcopyright} 2008 Springer-Verlag.",

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AU - Sanchón, Manel

AU - Urbano, José Miguel

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Y1 - 2008/8/1

N2 - The aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L1. © 2008 Springer-Verlag.

AB - The aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L1. © 2008 Springer-Verlag.

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JO - Monatshefte fur Mathematik

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ER -

The obstacle problem for nonlinear elliptic equations with variable growth and L1-data

Abstract

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ASJC Scopus subject areas

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