The obstacle problem for nonlinear degenerate equations with $L^{1}$-data

Jun Zheng; Binhua Feng; Zhihua Zhang

The obstacle problem for nonlinear degenerate equations with $L^{1}$-data

Analysis of PDEs 2015-11-25 v2 Functional Analysis

Authors: Jun Zheng , Binhua Feng , Zhihua Zhang

Abstract

The aim of this paper is to study the obstacle problem with an elliptic operator having degenerate coercivity. We prove the existence of an entropy solution to the obstacle problem under the assumption of $L^{1}-$ summability on the data. Meanwhile, we prove that every entropy solution belongs to some Sobolev space $W^{1,q}(\Omega)$ .

Keywords

elliptic partial differential equations partial differential equations parabolic partial differential equations

Cite

@article{arxiv.1504.03793,
  title  = {The obstacle problem for nonlinear degenerate equations with $L^{1}$-data},
  author = {Jun Zheng and Binhua Feng and Zhihua Zhang},
  journal= {arXiv preprint arXiv:1504.03793},
  year   = {2015}
}

Comments

21 pages. arXiv admin note: text overlap with arXiv:1003.2305 by other authors

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