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arXiv · 1003.1740

On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications

J. F. Rodrigues·R. Teymurazyan
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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 $C^{1,α}$ 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.

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J. F. Rodrigues, R. Teymurazyan. 2010-03-08. On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications. https://arxiv.org/abs/1003.1740

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