On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications
Analysis of PDEs
2010-03-10 v1 Mathematical Physics
math.MP
Optimization and Control
Abstract
We prove the Lewy-Stampacchia inequalities for the two obstacles problem in abstract form for T-monotone operators. As a consequence for a general class of quasi-linear elliptic operators of Ladyzhenskaya-Uraltseva type, including p(x)-Laplacian type operators, we derive new results of regularity for the solution. We also apply those inequalities to obtain new results to the N-membranes problem and the regularity and monotonicity properties to obtain the existence of a solution to a quasi-variational problem in (generalized) Orlicz-Sobolev spaces.
Cite
@article{arxiv.1003.1740,
title = {On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications},
author = {J. F. Rodrigues and R. Teymurazyan},
journal= {arXiv preprint arXiv:1003.1740},
year = {2010}
}