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The abstract Lewy-Stampacchia inequality and applications. (English. French summary) Zbl 1318.49016
The Lewy-Stampacchia inequality is a basic tool in the study of the solutions for the obstacle problem. The authors provide an abstract version of it in the setting of topological vector lattices using essentially the submodularity property of the functional. They show how the classical case can be recovered and give applications to fractional Laplacian, double obstacle problem and metric measure structures.

MSC:
49J40 Variational inequalities
35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators
35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
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