The obstacle problem for nonlinear elliptic equations with variable growth and L1-data

By J. Rodrigues, Manel Sanchón, José Miguel Urbano. 2008

58 citations recorded by the source corpus.

Abstract.The aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L1.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/02ee5079f05961c510aa1605ebfa1803517e4f16

Citations in the corpus

• Overview of differential equations with non-standard growth (2010, unknown): “[128] Henriques, E.; Urbano, J.M.: Intrinsic scaling for PDE’s with an exponential nonlinearity.”