@article{ASNSP_1995_4_22_2_241_0, author = {B\'enilan, Philippe and Boccardo, Lucio and Gallou\"et, Thierry and Gariepy, Ron and Pierre, Michel and Vazquez, Juan Luis}, title = {An $L^1$-theory of existence and uniqueness of solutions of nonlinear elliptic equations}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {241--273}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 22}, number = {2}, year = {1995}, mrnumber = {1354907}, zbl = {0866.35037}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1995_4_22_2_241_0/} }
TY - JOUR AU - Bénilan, Philippe AU - Boccardo, Lucio AU - Gallouët, Thierry AU - Gariepy, Ron AU - Pierre, Michel AU - Vazquez, Juan Luis TI - An $L^1$-theory of existence and uniqueness of solutions of nonlinear elliptic equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1995 SP - 241 EP - 273 VL - 22 IS - 2 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1995_4_22_2_241_0/ LA - en ID - ASNSP_1995_4_22_2_241_0 ER -
%0 Journal Article %A Bénilan, Philippe %A Boccardo, Lucio %A Gallouët, Thierry %A Gariepy, Ron %A Pierre, Michel %A Vazquez, Juan Luis %T An $L^1$-theory of existence and uniqueness of solutions of nonlinear elliptic equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1995 %P 241-273 %V 22 %N 2 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1995_4_22_2_241_0/ %G en %F ASNSP_1995_4_22_2_241_0
Bénilan, Philippe; Boccardo, Lucio; Gallouët, Thierry; Gariepy, Ron; Pierre, Michel; Vazquez, Juan Luis. An $L^1$-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 22 (1995) no. 2, pp. 241-273. http://www.numdam.org/item/ASNSP_1995_4_22_2_241_0/
[B1] Equations d'évolution dans un espace de Banach quelconque et applications. Thesis, Univ. Orsay, 1972.
,[B2] On the p-Laplacian in L1. Conference at the Analysis Seminar, Dept. of Math., Univ. Wisconsin at Madison, January 1987.
,[BBC] A semilinear equation in L1. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 (1975), 523-555. | Numdam | MR | Zbl
- - ,[BC] Completely accretive operators. In: "Semigroup Theory and Evolution Equations" (Ph. Clément et al. eds.), M. Dekker, 1991, 41-76. | MR | Zbl
- ,[BCP] Evolution Equations governed by accretive operators. To appear.
- - ,[BeW] Absorptions non linéaires. J. Funct. Anal. 114 (1993), 59-96. | MR | Zbl
- ,[BG1] Non linear elliptic and parabolic equations involving measure data. Jour. Funct. Anal. 87 (1989), 149-169. | MR | Zbl
- ,[BG2] Nonlinear elliptic equations with right-hand side measures. Comm. Partial Differential Equations 17 (1992), 641-655. | MR | Zbl
- ,[BGV] Nonlinear elliptic equations in R N without growth restrictions on the data. Jour. Diff. Eqns. 105 (1993), 334-363. | MR | Zbl
- - ,[BGDM] Existence of a solution for a weaker form of a nonlinear elliptic equation. In: "Recent advances in nonlinear elliptic and parabolic problems" (Nancy, 1988), Pitman Res. Notes Math. Ser. 208, Longman Sc. Tech., Harlow, 1989, 229-246. | MR | Zbl
- - - ,[Br] Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert. North Holland, Amsterdam, 1973. | Zbl
,[BS] Semilinear elliptic equations in L 1. Jour. Math. Soc. Japan 25 (1973), 565-590. | MR | Zbl
- ,[Bw] Pseudomonotone operators and nonlinear elliptic boundary-value problems on unbounded domains. Proc. Nat. Acad. Sci. 74 (1977), 2659-2661. | MR | Zbl
,[C] An introduction to evolution governed by accretive operators. In: "Dynamical Systems, An International Symposium ", vol. 1 (L. Cesari et al. eds.), Academic Press, New York, 1976, 131-165. | MR | Zbl
,[D] Alcuni problemi relativi alla H -convergenza di equazioni ellittiche e paraboliche quasilineari. Doctoral Thesis, Roma 1, 1992 (in Italian).
,[DBH1] On the Cauchy problem and initial traces for a degenerate parabolic equation. Trans. Amer. Math. Soc. 314 (1989), 187-224. | MR | Zbl
- ,[DBH2] Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when 1 < p < 2. Arch. Rat. Mech. Anal. 111 (1990), 225-290. | MR | Zbl
- ,[DL] On the Cauchy problem for Boltzman equations: Global existence and weak stability. Ann of Math. 130 (1989), 321-366. | MR | Zbl
- ,[GT] Elliptic Partial Differential Equations of Second Order. Springer, Berlin, 1983. | MR | Zbl
- ,[K] Topological Methods in the Theory of Nonlinear Integral Equations. Pergamon Press, Oxford, 1965. | MR | Zbl
,[Kr] First-order quasilinear equations in several independent variables. Mat. USSR-Sbornik 10 (1970), 217-243. | Zbl
,[La] Hyperbolic systems of conservation laws, II. Comm. Pure Applied Maths 10 (1957), 537-566. | MR | Zbl
,[Li] Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris, 1969. | MR | Zbl
,[LL] Quelques résultats de Vishik sur les problèmes elliptiques semi-linéaires par les méthodes de Minty et Browder. Bull. Soc. Math. France 93 (1965), 97-107. | Numdam | MR | Zbl
- ,[LM] Sur les solutions renormalisées d' équations elliptiques non linéaires, to appear.
- ,[M] Soluciones renormalizadas de EDP elipticas no lineales. Publ. Laboratoire d'Analyse Numérique, Univ. Paris 6, R 93023 (1993) [in Spanish].
,[R1] Resolution of the critical cases for problems with L1-data. Asymptotic Analysis 6 (1993), 229-246. | MR | Zbl
,[R2] Generalized solutions in a new type of sets for problems with measures as data. Diff. Int. Equations 6 (1993), 27-36. | MR | Zbl
,[R3] Uniqueness of renormalized solutions in a T-set for the L1-data problem and the link between various formulations. Indiana Univ. Math. J. 43 2 (1994), 285-293. | MR | Zbl
,[S] Pathological solution of elliptic differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964), 385-387. | Numdam | MR | Zbl
,[Ta] Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces. Annali Mat. Pura Appl. 120 (1979), 159-184. | MR | Zbl
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