In this paper we prove that at least one solution of the obstacle problem for a linear elliptic operator perturbed by a nonlinearity having quadratic growth in the gradient satisfies the Lewy-Stampacchia inequality.Résumé. Nous démontrons dans cet article qu'au moins une solution du problème de l'obstacle pour un opérateur elliptique linéaire perturbé par une non linéarité à croissance quadratique par rapport au gradient vérifie l'inégalité de Lewy-Stampacchia.
The main aim of this paper is to extend to the case of a pseudomonotone operator Lewy-Stampacchia’s inequality proposed by F. Donati [7] in the framework of monotone operators. For that, an ad hoc type of perturbation of the operator is proposed.
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