@article{ASNSP_1999_4_28_4_741_0,
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},
year = {1999},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 28},
number = {4},
mrnumber = {1760541},
zbl = {0958.35045},
language = {en},
url = {https://www.numdam.org/item/ASNSP_1999_4_28_4_741_0/}
}
TY - JOUR AU - Dal Maso, Gianni AU - Murat, François AU - Orsina, Luigi AU - Prignet, Alain TI - Renormalized solutions of elliptic equations with general measure data JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1999 SP - 741 EP - 808 VL - 28 IS - 4 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1999_4_28_4_741_0/ LA - en ID - ASNSP_1999_4_28_4_741_0 ER -
%0 Journal Article %A Dal Maso, Gianni %A Murat, François %A Orsina, Luigi %A Prignet, Alain %T Renormalized solutions of elliptic equations with general measure data %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1999 %P 741-808 %V 28 %N 4 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1999_4_28_4_741_0/ %G en %F ASNSP_1999_4_28_4_741_0
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. https://www.numdam.org/item/ASNSP_1999_4_28_4_741_0/
[1] - - - - - , An L1 theory of existence and uniqueness of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995), 241-273. | Zbl | MR | Numdam
[2] , Elliptic and parabolic differential problems with measure data., Boll. Un. Mat. Ital. 11 (1997), 439-461. | Zbl | MR
[3] - , Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989), 149-169. | Zbl | MR
[4] - , Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations 17 (1992), 641-655. | Zbl | MR
[5] - - , Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), 539-551. | Zbl | MR | Numdam
[6] - , Remarques sur l'homogénéisation de certains problèmes quasilinéaires, Portugaliae Math. 41 (1982), 535-562. | Zbl | MR
[7] - , Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal. 19 (1992), 581-597. | Zbl | MR
[8] - , 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. | Zbl | MR
[9] , 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. | Zbl | MR
[10] - , Some properties of reachable solutions of nonlinear elliptic equations with measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997), 375-396. | Zbl | MR | Numdam
[11] - - - , 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. | Zbl | MR
[12] - - , 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] - , 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] - - , On the closable part of pre-Dirichlet forms and the fine support of the underlying measures, Osaka J. Math. 28 (1991), 517-535. | Zbl | MR
[15] - , Existence of a solution to a coupled elliptic system, Appl. Math. Letters 7 (1994), 49-55. | Zbl | MR
[16] - - , Inverting the p-harmonic operator, Manuscripta Math. 92 (1997), 249-258. | Zbl | MR
[17] - - , "Nonlinear Potential Theory of Degenerate Elliptic Equations", Oxford University Press, 1993. | Zbl | MR
[18] , Quasilinear problems with singularities, Manuscripta Math. 57 (1987), 281-313. | Zbl | MR
[19] - , Singular solutions of the p-Laplace equation, Math. Ann. 275 (1986), 599-615. | Zbl | MR
[20] - , Entropy solutions for nonlinear elliptic equations in L1, Nonlinear Anal. 32 (1998), 325-334. | Zbl | MR
[21] - , Quelques résultats de višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France 93 (1965), 97-107. | Zbl | MR | Numdam
[22] , "Quelques méthodes de résolution des problèmes aux limites non linéaires", Dunod et Gauthier-Villars, Paris, 1969. | Zbl | MR
[23] - , Solutions renormalisées d'équations elliptiques non linéaires, to appear.
[24] - , Nemitsky operators on Sobolev spaces, Arch. Rational Mech. Anal. 51 (1973), 347-370. | Zbl | MR
[25] , Soluciones renormalizadas de EDP elipticas no lineales, Preprint 93023, Laboratoire d'Analyse Numérique de l'Université Paris VI (1993).
[26] , 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] , Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat. 15 (1995), 321-337. | Zbl | MR
[28] , Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964), 385-387. | Zbl | MR | Numdam
[29] , Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1965), 189-258. | Zbl | MR | Numdam
