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

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 $W^{1,q}(\Omega )$.

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

References in corpus (2)

• The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity
• Existence of solutions for some noncercive elliptic problems involving derivatives of nonlinear terms