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ENTROPY AND RENORMALIZED SOLUTIONS FOR THE p(x)-LAPLACIAN EQUATION WITH MEASURE DATA

Part of: Linear function spaces and their duals Elliptic equations and systems

Published online by Cambridge University Press:  18 August 2010

CHAO ZHANG  and
SHULIN ZHOU
CHAO ZHANG*
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China (email: czhang@math.pku.edu.cn)
SHULIN ZHOU
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China (email: szhou@math.pku.edu.cn)
*
✉For correspondence; e-mail: czhang@math.pku.edu.cn
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Abstract

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In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L1(Ω)+W−1,p′(⋅)(Ω). Moreover, we obtain the equivalence of entropy solutions and renormalized solutions.

Keywords

variable exponentsentropy solutionsrenormalized solutionsexistenceuniqueness

MSC classification

Secondary: 35J70: Degenerate elliptic equations 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 3 , December 2010 , pp. 459 - 479
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This work was supported in part by the NBRPC under Grant 2006CB705700 and the NSFC under Grant 10990013.

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