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