Electron. J. Diff. Equ., Vol. 2014 (2014), No. 92, pp. 1-14.

Entropy solutions for nonlinear elliptic equations with variable exponents

Chao Zhang

In this article we prove the existence and uniqueness of entropy solutions for p(x)-Laplace equations with a Radon measure which is absolutely continuous with respect to the relative p(x)-capacity. Moreover, the existence of entropy solutions for weighted p(x)-Laplace equation is also obtained.

Submitted August 26, 2013. Published March 4, 2014.
Math Subject Classifications: 35J70, 35D05, 35D10, 46E35.
Key Words: Variable exponents; entropy solutions; existence; uniqueness.

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Chao Zhang
Department of Mathematics
Harbin Institute of Technology
Harbin 150001, China
email: czhangmath@hit.edu.cn

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