Lewy-Stampacchia Inequality in Quasilinear Unilateral Problems and Application to the G-convergence

Lucio Boccardo

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 2, page 275-282
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Boccardo, Lucio. "Lewy-Stampacchia Inequality in Quasilinear Unilateral Problems and Application to the G-convergence." Bollettino dell'Unione Matematica Italiana 4.2 (2011): 275-282. <http://eudml.org/doc/290735>.

@article{Boccardo2011,
abstract = {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.},
author = {Boccardo, Lucio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {275-282},
publisher = {Unione Matematica Italiana},
title = {Lewy-Stampacchia Inequality in Quasilinear Unilateral Problems and Application to the G-convergence},
url = {http://eudml.org/doc/290735},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Boccardo, Lucio
TI - Lewy-Stampacchia Inequality in Quasilinear Unilateral Problems and Application to the G-convergence
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/6//
PB - Unione Matematica Italiana
VL - 4
IS - 2
SP - 275
EP - 282
AB - 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.
LA - eng
UR - http://eudml.org/doc/290735
ER -

References

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  1. BENSOUSSAN, A. - BOCCARDO, L. - MURAT, F., On a nonlinear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. H. Poincaré Anal. non lin.5 (1988), 347-364. Zbl0696.35042MR963104
  2. BENSOUSSAN, A. - BOCCARDO, L. - MURAT, F., Homogenization of elliptic equations with principal part not in divergence form and Hamiltonian with quadratic growth, Comm. Pure Appl. Math., 39 (1986), 769-805. Zbl0602.35030MR859273DOI10.1002/cpa.3160390604
  3. BENSOUSSAN, A. - BOCCARDO, L. - MURAT, F., H-convergence for quasilinear elliptic equations with quadratic growth, Appl. Math. Opt., 26 (1992), 253-272. Zbl0795.35008MR1175481DOI10.1007/BF01371084
  4. BENSOUSSAN, A. - BOCCARDO, L. - DALL'AGLIO, A. - MURAT, F., H-convergence for quasilinear elliptic equations, in Composite media and homogenization theory, G. Dal Maso and G. Dell'Antonio ed., World Scientific, 1995. MR1145740DOI10.1007/978-1-4684-6787-1
  5. BOCCARDO, L. - CAPUZZO DOLCETTA, I., G-convergenza e problema di Dirichlet unilaterale, Boll. UMI12 (1975), 115-123. MR399988
  6. BOCCARDO, L. - CIRMI, R., Existence and uniqueness of solutions of unilateral problems with L 1 data, J. Convex Anal., 6 (1999), 195-206. Zbl0958.47038MR1713958
  7. BOCCARDO, L. - MURAT, F. - PUEL, J.-P., Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl., 152 (1988), 183-196. Zbl0687.35042MR980979DOI10.1007/BF01766148
  8. BOCCARDO, L. - MURAT, F. - PUEL, J.-P., Resultats d'existence pour certains problèmes elliptiques quasi linéaires, Ann. Sc. Norm. Sup. Pisa, 11 (1984), 213-235. Zbl0557.35051MR764943
  9. BOCCARDO, L. - MURAT, F. - PUEL, J.-P., LI-estimates for some nonlinear partial differential equations and application to an existence result, SIAM J. Math. Anal., 23 (1992), 326-333. Zbl0785.35033MR1147866DOI10.1137/0523016
  10. BRAUNER, C. - NIKOLAENKO, B., 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. MR670269
  11. LEWY, H. - STAMPACCHIA, G., On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), 153-188. Zbl0167.11501MR247551DOI10.1002/cpa.3160220203
  12. MOKRANE, A. - MURAT, F., The Lewy-Stampacchia inequality for the obstacle problem with quadratic growth in the gradient, Ann. Mat. Pura Appl., 184 (2005), 347-360. Zbl1105.35041MR2164262DOI10.1007/s10231-004-0120-x
  13. MURAT, F. - TARTAR, L., H-Convergence; in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev, R. Kohn, editors, Birkhäuser, Boston (1997), 21-43. MR1493039
  14. MOSCO, U. - TROIANIELLO, G., On the smoothness of solutions of unilateral Dirichlet problems, Boll. Un. Mat. Ital., 8 (1973), 57-67. Zbl0277.35033MR390479
  15. PALMERI, M. C., Homographic approximation applied to nonlinear elliptic unilateral problems, Rend. Mat. Appl., 17 (1997), 387-402. Zbl0902.35046MR1608700
  16. PALMERI, M. C., Homographic approximation for some nonlinear parabolic unilateral problems, J. Convex Anal., 7 (2000), 353-373. Zbl0972.35059MR1811685
  17. SPAGNOLO, S., Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa, 22 (1968), 577-597. MR240443
  18. STAMPACCHIA, G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. Zbl0151.15401MR192177

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