In this paper we prove uniqueness results for the renormalized solution, if it exists, of a class of non coercive nonlinear problems whose prototype is
Keywords: uniqueness, nonlinear elliptic equations, noncoercive problems, data in $L^1$
@article{COCV_2002__8__239_0, author = {Betta, M. F. and Mercaldo, A. and Murat, F. and Porzio, M. M.}, title = {Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^1(\Omega )$}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {239--272}, publisher = {EDP-Sciences}, volume = {8}, year = {2002}, doi = {10.1051/cocv:2002051}, mrnumber = {1932952}, zbl = {1092.35032}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2002051/} }
TY - JOUR AU - Betta, M. F. AU - Mercaldo, A. AU - Murat, F. AU - Porzio, M. M. TI - Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^1(\Omega )$ JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 239 EP - 272 VL - 8 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2002051/ DO - 10.1051/cocv:2002051 LA - en ID - COCV_2002__8__239_0 ER -
%0 Journal Article %A Betta, M. F. %A Mercaldo, A. %A Murat, F. %A Porzio, M. M. %T Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^1(\Omega )$ %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 239-272 %V 8 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2002051/ %R 10.1051/cocv:2002051 %G en %F COCV_2002__8__239_0
Betta, M. F.; Mercaldo, A.; Murat, F.; Porzio, M. M. Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^1(\Omega )$. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), pp. 239-272. doi : 10.1051/cocv:2002051. http://archive.numdam.org/articles/10.1051/cocv:2002051/
[1] An -theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995) 241-273. | Numdam | MR | Zbl
, , , , and ,[2] Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum. C. R. Acad. Sci. Paris Sér. I Math. 332 (to appear). | MR | Zbl
, , and ,[3] Existence of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side measure. J. Math. Pures Appl. (to appear). | MR
, , and ,[4] Uniqueness results for nonlinear elliptic equations with a lower order term (to appear). | MR | Zbl
, , and ,[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. | Numdam | MR | Zbl
, and ,[6] Problema di Dirichlet per equazioni ellittiche di tipo variazionale su insiemi non limitati. Boll. Un. Mat. Ital. 8 (1973) 46-56. | MR | Zbl
and ,[7] Approximated solutions of equations with data. Application to the -convergence of quasi-linear parabolic equations. Ann. Mat. Pura Appl. 170 (1996) 207-240. | Zbl
,[8] Renormalized solutions for elliptic equations with general measure data. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999) 741-808. | Numdam | MR | Zbl
, , and ,[9] Uniqueness and maximal regularity for nonlinear elliptic systems of -Laplace type with measure valued right-hand side. J. Reine Angew. Math. 520 (2000) 1-35. | MR | Zbl
, and ,[10] Existence and uniqueness results for solutions of nonlinear equations with right-hand side in . Studia Math. 127 (1998) 223-231. | MR | Zbl
and ,[11] Inverting the p-harmonic operator. Manuscripta Math. 92 (1997) 249-258. | MR | Zbl
, and ,[12] Remarks on the uniqueness of comparable renormalized solutions of elliptic equations with measure data. Ann. Mat. Pura Appl. Ser. IV 180 (2002) 441-449. | MR | Zbl
,[13] Solutions renormalisées d'équations elliptiques non linéaires (to appear).
and ,[14] Soluciones renormalizadas de EDP elipticas no lineales, Preprint 93023. Laboratoire d'Analyse Numérique de l'Université Paris VI (1993).
,[15] Équations elliptiques non linéaires avec second membre ou mesure, in Actes du 26 Congrès National d'Analyse Numérique. Les Karellis, France (1994) A12-A24.
,[16] Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures. Rend. Mat. Appl. 15 (1995) 321-337. | MR | Zbl
,[17] Pathological solutions of elliptic differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964) 385-387. | Numdam | MR | Zbl
,[18] 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
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