Existence results for semilinear elliptic equations with small measure data
Grenon, Nathalie
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002), p. 1-11 / Harvested from Numdam
Publié le : 2002-01-01
@article{AIHPC_2002__19_1_1_0,
     author = {Grenon, Nathalie},
     title = {Existence results for semilinear elliptic equations with small measure data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {19},
     year = {2002},
     pages = {1-11},
     mrnumber = {1902548},
     zbl = {1011.35054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2002__19_1_1_0}
}
Grenon, Nathalie. Existence results for semilinear elliptic equations with small measure data. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) pp. 1-11. http://gdmltest.u-ga.fr/item/AIHPC_2002__19_1_1_0/

[1] Adams D.R., Pierre M., Capacitary strong type estimates in semilinear problems, Ann. Inst. Fourier, Grenoble 41 (1991) 117-135. | Numdam | MR 1112194 | Zbl 0741.35012

[2] Baras P., Pierre M., Critère d'existence de solutions positives pour des équations semilinéaires non monotones, Ann. Inst. H. Poincaré, Analyse Non Linéaire 2 (1985) 185-212. | Numdam | MR 797270 | Zbl 0599.35073

[3] Benilan P., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J.L., An L1 theory of existence uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995) 241-273. | Numdam | MR 1354907 | Zbl 0866.35037

[4] Brezis H., Cabré X., Some simple nonlinear PDE's without solutions, Bolletino U.M.I. 1-B (1998) 223-262. | MR 1638143 | Zbl 0907.35048

[5] Boccardo L., Gallouët T., Orsina L., Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 539-551. | Numdam | MR 1409661 | Zbl 0857.35126

[6] Boccardo L., Murat F., Puel J.P., Existence of bounded solutions for nonlinear elliptic unilateral problem, Ann. di Mat. Pura ed Appl. 152 (1988) 183-196. | MR 980979 | Zbl 0687.35042

[7] Dal Maso G., Murat F., Orsina L., Prignet A., Definition and existence of renormalized solutions of elliptic equations with general measure data, C. R. Acad. Sci. Paris Série I 325 (1997) 481-486. | MR 1692311 | Zbl 0887.35057

[8] Dal Maso G., Murat F., Orsina L., Prignet A., Renormalized solutions of elliptic equations with general measure data, Ann. Scuol. Norm. Pisa (4) XXVIII (1999) 741-808. | Numdam | MR 1760541 | Zbl 0958.35045

[9] Ferone V., Murat F., Nonlinear problems having natural growth in the gradient: an existence result when the source term is small, to appear. | MR 1780731 | Zbl 01529452

[10] Fukushima M., Sato K., Taniguchi S., On the closable part of pre-Dirichlet forms and the fine support of the underlying measures, Osaka J. Math. 28 (1991) 517-535. | MR 1144471 | Zbl 0756.60071

[11] Kalton N.J., Verbitsky E., Nonlinear equations and weighted norm inequalities, Trans. Amer. Math. Soc. 351 (9) 3441-3497. | MR 1475688 | Zbl 0948.35044

[12] Grenon N., Existence and comparison results quasilinear elliptic equations with quadratic growth in the gradient, J. Differential Equations, to appear. | MR 1816791

[13] Grenon N., Lr estimates for degenerate elliptic problems, Pot. Anal., to appear. | MR 1894505 | Zbl 1014.35035

[14] Grenon-Isselkou N., Mossino J., Existence de solutions bornées pour certaines équations elliptiques quasilinéaires, C. R. Acad. Sci. 321 (1995) 51-56. | MR 1340081 | Zbl 0837.35045

[15] Orsina L., Solvability of linear and semilinear eigenvalue problems with L1 data, Rend. Sem. Mat. Univ. Padova 90 (1993). | Numdam | MR 1257140 | Zbl 0822.35106

[16] Stampacchia G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1965) 189-258. | Numdam | MR 192177 | Zbl 0151.15401

[17] Talenti G., Linear elliptic P.D.E.'s: Level sets, rearrangements and a priori estimates of solutions, Boll. U.M.I. (6) 4-B (1985) 917-949. | MR 831299 | Zbl 0602.35025