Abstract
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.
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Mathematics Subject Classification (2000)
35J85, 47J20
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Mokrane, A., Murat, F. The Lewy–Stampacchia inequality for the obstacle problem with quadratic growth in the gradient. Annali di Matematica 184, 347–360 (2005). https://doi.org/10.1007/s10231-004-0120-x
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DOI: https://doi.org/10.1007/s10231-004-0120-x