Geodesic
Lewy-Stampacchia Inequality in Quasilinear Unilateral Problems and Application to the G-convergence
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 275-282.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In the paper [5] in collaboration with Italo Capuzzo Dolcetta, the use of the Lewy-Stampacchia inequality was the main tool for the study of the G-convergence in unilateral problems with linear differential operators. In this paper we prove a Lewy-Stampacchia inequality for unilateral problems with more general differential operators (quasilinear operators with lower order term having quadratic growth with respect to the gradient) in order to study the G-convergence in unilateral problems with such type of differential operators. 
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Boccardo, Lucio. Lewy-Stampacchia Inequality in Quasilinear Unilateral Problems and Application to the G-convergence. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 275-282. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a7/

[1] A. Bensoussan - L. Boccardo - F. Murat, On a nonlinear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. H. Poincaré Anal. non lin. 5 (1988), 347-364. | fulltext EuDML | MR | Zbl

[2] A. Bensoussan - L. Boccardo - F. Murat, Homogenization of elliptic equations with principal part not in divergence form and Hamiltonian with quadratic growth, Comm. Pure Appl. Math., 39 (1986), 769-805. | DOI | MR | Zbl

[3] A. Bensoussan - L. Boccardo - F. Murat, H-convergence for quasilinear elliptic equations with quadratic growth, Appl. Math. Opt., 26 (1992), 253-272. | DOI | MR | Zbl

[4] A. Bensoussan - L. Boccardo - A. Dall'Aglio - F. Murat, H-convergence for quasilinear elliptic equations, in Composite media and homogenization theory, G. Dal Maso and G. Dell'Antonio ed., World Scientific, 1995. | DOI | MR

[5] L. Boccardo - I. Capuzzo Dolcetta, G-convergenza e problema di Dirichlet unilaterale, Boll. UMI 12 (1975), 115-123. | MR

[6] L. Boccardo - R. Cirmi, Existence and uniqueness of solutions of unilateral problems with $L^1$ data, J. Convex Anal., 6 (1999), 195-206. | fulltext EuDML | MR | Zbl

[7] L. Boccardo - F. Murat - J.-P. Puel, Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl., 152 (1988), 183-196. | DOI | MR | Zbl

[8] L. Boccardo - F. Murat - J.-P. Puel, Resultats d'existence pour certains problèmes elliptiques quasi linéaires, Ann. Sc. Norm. Sup. Pisa, 11 (1984), 213-235. | fulltext EuDML | MR | Zbl

[9] L. Boccardo - F. Murat - J.-P. Puel, LI-estimates for some nonlinear partial differential equations and application to an existence result, SIAM J. Math. Anal., 23 (1992), 326-333. | DOI | MR | Zbl

[10] C. Brauner - B. Nikolaenko, Homographic approximations of free boundary problems characterized by elliptic variational inequalities. In Nonlinear partial differential equations and their applications, Collège de France Seminar Vol. III, ed. by H. Brezis and J. L. Lions, Research Notes in Math., 70, Pitman, London (1982), 86-128. | MR

[11] H. Lewy - G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), 153-188. | DOI | MR | Zbl

[12] A. Mokrane - F. Murat, The Lewy-Stampacchia inequality for the obstacle problem with quadratic growth in the gradient, Ann. Mat. Pura Appl., 184 (2005), 347-360. | DOI | MR | Zbl

[13] F. Murat - L. Tartar, H-Convergence; in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev, R. Kohn, editors, Birkhäuser, Boston (1997), 21-43. | MR

[14] U. Mosco - G. Troianiello, On the smoothness of solutions of unilateral Dirichlet problems, Boll. Un. Mat. Ital., 8 (1973), 57-67. | MR | Zbl

[15] M. C. Palmeri, Homographic approximation applied to nonlinear elliptic unilateral problems, Rend. Mat. Appl., 17 (1997), 387-402. | MR | Zbl

[16] M. C. Palmeri, Homographic approximation for some nonlinear parabolic unilateral problems, J. Convex Anal., 7 (2000), 353-373. | MR | Zbl

[17] S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa, 22 (1968), 577-597. | fulltext EuDML | MR

[18] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. | fulltext EuDML | MR | Zbl