Existence and regularity results for nonlinear elliptic equations with measure data

Advances in Differential Equations

Volumn 1, Issue 5, 1996, Pages 899-917

  Del Vecchio, T ^a   Posteraro, M R ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000871531     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. A. Alvino, P.L. Lions, and G. Trombetti, Comparison results for elliptic and parabolic equations via Schwartz symmetrization, Ann. Inst. Henry Poincaré, 7 (1990), 37-65.
2. A. Alvino and G. Trombetti, Sulle migliori costanti di maggiorazione per una classe di equazioni ellittiche degeneri, Ricerche Mat., 27 (1978),413-428.
3. H. Brezis, Nonlinear elliptic equations involving measures, in "Contributions to Nonlinear Partial Differential Equations," C. Bardos, A. Damlamian, J.I. Diaz and J. Hernandez, Pitman Research Notes in Mathematics, Series 89, (1983), 82-89.
4. P. Benilan, H. Brezis, and M. Crandall, A semilinear equation in L1, Ann. Scuola Norm. Sup. Pisa, 2 (1975), 523-555.
5. E. Beckenback and R. Bellman, "Inequalities," Springer-Verlag, 1965.
6. M.F. Betta, V. Ferone, and A. Mercaldo, Regularity for solutions of nonlinear elliptic equations, Bull. Sc. Math., to appear.
7. L. Boccardo and T. Gallouet, Nonlinear elliptic and parabolic equations involving measure data, J. Functional Analysis, 87 (1989), 149-169.
8. L. Boccardo and T. Gallouet, Nonlinear elliptic equations with right hand side measure, Comm. in P.D.E., 17 (1992), 641-654.
9. L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Analysis, TMA, 19 (1992), 581-597.
10. L. Boccardo, F. Murat, and J. P. Puel, Rèsultats d'existence pour certains problémes elliptiques quasilinèaires, Ann. Scuola Norm. Sup. Pisa, 11 (1984), 213-235.
11. L. Boccardo, F. Murat, and J.P. Puel, Existence of bounded solutions for nonlinear elliptic problems, Ann. Mat. Pura e Appl., (IV), CLII (1988), 183-196.
12. C. Bennett and K. Rudnik, "On Lorentz-Zygmund Spaces," Dissertaziones Mathematcae, Polska AKademia Nauk, Instytut Matematyczny, Warszawa, 1980.
13. C. Bennett and R. Sharpley, "Interpolation of Operators," Academic Press, 1988.
14. H. Brezis and W. Strauss, Semilinear elliptic equations in L1, J. Math. Soc. Japan, 25 (1973), 565-590.
15. T. Del Vecchio, Nonlinear elliptic equation with measure data, Potential Analysis, 4 (1995), 185-203.
16. T. Gallouet and J.M. Morel, On some semilinear problems in L1, Boll. Un. Mat. Ital. (6) 4-A (1985), 121-131.
17. G.H. Hardy, J.E. Littlewood, and G. Polya, "Inequalities," Cambridge University Press, Cambridge, (1964).
18. J.L. Lions, "Quelques méthodes de Rèsolution des Problèmes aux Limites Nonlinéaires," Dunod, Paris, 1969.
19. J. Liang, Weakly-coercive quasilinear elliptic equations with inhomogeneous measure data, in Progress in Partial Differential Equation: Elliptic and parabolic problems (Edited by Bandle et al.), Pitman research Notes in Mathematics, N. 266, p. 182-192, Longman, Harlow (1992).
20. V.G. Maz'ja, On weak solutions of the Dirichlet and Neumann problems, Trans. Moscow Math. Soc., 20 (1969), 135-172.
21. J.M. Rakotoson, Quasilinear elliptic problems with measures as data, Differential and Integral Equations, 4 (1991), 449-457.
22. J.M. Rakotoson and R. Temam, Relative rearrangement in quasilinear elliptic variational inequalities, Indiana Univ. Math. J., 36 (1987), 757-810.
23. G. Stampacchia, Le probléme de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier Grenoble, 15 (1965), 189-258.
24. G. Talenti, Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa, (4) 3 (1976), 697-718.
25. G. Talenti, Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces, Ann. Mat. Pura e Applicata, (4) 120 (1979), 159-184.
26. G. Talenti, Linear elliptic P.D.E.'s: Level sets, rearrangements and apriori estimates of solutions, Boll. Un. Mat. Ital., (6) 4-B, (1985), 917-949.