Renormalized solutions of elliptic equations with general measure data
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 4, pp. 741-808.
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     author = {Dal Maso, Gianni and Murat, Fran\c{c}ois and Orsina, Luigi and Prignet, Alain},
     title = {Renormalized solutions of elliptic equations with general measure data},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {741--808},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {4},
     year = {1999},
     mrnumber = {1760541},
     zbl = {0958.35045},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_4_741_0/}
}
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Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain. Renormalized solutions of elliptic equations with general measure data. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 4, pp. 741-808. http://www.numdam.org/item/ASNSP_1999_4_28_4_741_0/

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

[2] L. Boccardo, Elliptic and parabolic differential problems with measure data., Boll. Un. Mat. Ital. 11 (1997), 439-461. | MR | Zbl

[3] L. Boccardo - T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989), 149-169. | MR | Zbl

[4] L. Boccardo - T. Gallouët, Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations 17 (1992), 641-655. | MR | Zbl

[5] L. Boccardo - T. Gallouët - L. Orsina, 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 | Zbl

[6] L. Boccardo - F. Murat, Remarques sur l'homogénéisation de certains problèmes quasilinéaires, Portugaliae Math. 41 (1982), 535-562. | MR | Zbl

[7] L. Boccardo - F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal. 19 (1992), 581-597. | MR | Zbl

[8] D. Cioranescu - F. Murat, Un terme étrange venu d'ailleurs I & II, In: "Nonlinear partial differential equations and their applications" Collège de France Seminar, Vol. II & III, H. Brezis and J.-L. Lions (eds.), Research Notes in Math. 60 & 70, Pitman, Boston (1982), 98-138, 154-178. English translation: A strange term coming from nowhere, In: "Topics in the mathematical modelling of composite materials", 45-93, Progr. Nonlinear Differential Equations Appl. 31, Birkhäuser Boston, Boston, 1997. | MR | Zbl

[9] A. Dall'Aglio, Approximated solutions of equations with L 1 data. Application to the H-convergence of parabolic quasi-linear equations, Ann. Mat. Pura Appl. 170 (1996), 207-240. | MR | Zbl

[10] G. Dal Maso - A. Malusa, Some properties of reachable solutions of nonlinear elliptic equations with measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997), 375-396. | Numdam | MR | Zbl

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

[12] G. Dolzmann - N. Hungerbühler - S. Muller, Uniqueness and maximal regularity for nonlinear elliptic systems of n-Laplace type with measure valued right hand side, Preprint 20, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig (1998). | MR

[13] A. Fiorenza - C. Sbordone, Existence and uniqueness results for solutions of nonlinear equations with right-hand side in L 1 (Ω), Studia Math. 127 (1998), 223-231. | Zbl

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

[15] T. Gallouët - R. Herbin, Existence of a solution to a coupled elliptic system, Appl. Math. Letters 7 (1994), 49-55. | MR | Zbl

[16] L. Greco - T. Iwaniec - C. Sbordone, Inverting the p-harmonic operator, Manuscripta Math. 92 (1997), 249-258. | MR | Zbl

[17] J. Heinonen - T. Kilpeläinen - O. Martio, "Nonlinear Potential Theory of Degenerate Elliptic Equations", Oxford University Press, 1993. | MR | Zbl

[18] S. Kichenassamy, Quasilinear problems with singularities, Manuscripta Math. 57 (1987), 281-313. | MR | Zbl

[19] S. Kichenassamy - L. Veron, Singular solutions of the p-Laplace equation, Math. Ann. 275 (1986), 599-615. | MR | Zbl

[20] C. Leone - A. Porretta, Entropy solutions for nonlinear elliptic equations in L1, Nonlinear Anal. 32 (1998), 325-334. | MR | Zbl

[21] J. Leray - J.-L. Lions, Quelques résultats de višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France 93 (1965), 97-107. | Numdam | MR | Zbl

[22] J.-L. Lions, "Quelques méthodes de résolution des problèmes aux limites non linéaires", Dunod et Gauthier-Villars, Paris, 1969. | MR | Zbl

[23] P.-L. Lions - F. Murat, Solutions renormalisées d'équations elliptiques non linéaires, to appear.

[24] M. Marcus - V.J. Mizel, Nemitsky operators on Sobolev spaces, Arch. Rational Mech. Anal. 51 (1973), 347-370. | MR | Zbl

[25] F. Murat, Soluciones renormalizadas de EDP elipticas no lineales, Preprint 93023, Laboratoire d'Analyse Numérique de l'Université Paris VI (1993).

[26] F. Murat, Équations elliptiques non linéaires avec second membre L1 ou mesure, Actes du 26ème Congrés National d'Analyse Numérique, Les Karellis, France (1994), A12-A24.

[27] A. Prignet, Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat. 15 (1995), 321-337. | MR | Zbl

[28] J. Serrin, Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964), 385-387. | Numdam | MR | Zbl

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