Abstract

We prove the existence and uniqueness of renormalized solutions to a class of nonlinear elliptic equations with variable exponents and measure data in L1(Ω)+W−1,p′(⋅)(Ω)L^{1}(\Omega)+W^{-1,p'(\cdot)}(\Omega).

Author information

Contact details are reproduced from the original publication and may be historical.

Boqiang Lv

Key Laboratory of Poyang Lake Environment and Resource Utilization, Nanchang University, Ministry of Education, Nanchang, 33047, China
and: College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, China

lbq86@yahoo.com.cn

Fengquan Li

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

fqli@dlut.edu.cn

Weilin Zou

College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, China

zwl267@yahoo.com.cn

Keywords

  • Nonlinear elliptic equations
  • variable exponents
  • measure data
  • renormalized solution
  • existence
  • uniqueness

Mathematics Subject Classification

35D05, 35J60, 35J70, 26D07

Suggested citation

B. Lv, F. Li, W. Zou. “Existence and Uniqueness of Renormalized Solutions to Some Nonlinear Elliptic Equations with Variable Exponents and Measure Data.” Journal of Convex Analysis 21 (2014), No. 2, 317–338. https://doi.org/10.68381/jca21018

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.