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

2010/03/08 by José Francisco Rodrigues, Rafayel Teymurazyan, Rodrigues, J. F. +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1003.1740

openalex publication_date 2010/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Homogenization of obstacle problems in Orlicz-Sobolev spaces
• Monotone iterations of two obstacle problems with different operators
• Riesz potential estimates for double obstacle problems with Orlicz growth
• Gradient potential estimates for elliptic double obstacle problems with Orlicz growth
• Multiple solutions for two classes of quasilinear problems defined on a nonreflexive Orlicz-Sobolev space