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New existence and regularity results are given for non-linear elliptic problems with measure data. The gradient of the solution is itself in an optimal (fractional) Sobolev space: this can be considered an extension of Calderón–Zygmund theory to measure data problems.
On établit de nouveaux résultats d'existence et régularité pour des problèmes elliptiques non-linéaires avec données mesures. Le gradient de la solution appartient lui-même à un espace de Sobolev (fractionnaire) optimal, ce que l'on peut considérer comme une extension de la théorie de Calderón–Zygmund aux problèmes avec données mesures.
Mingione, Giuseppe 1
@article{CRMATH_2007__344_7_437_0,
author = {Mingione, Giuseppe},
title = {Calder\'on{\textendash}Zygmund estimates for measure data problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {437--442},
publisher = {Elsevier},
volume = {344},
number = {7},
year = {2007},
doi = {10.1016/j.crma.2007.02.005},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.02.005/}
}
TY - JOUR AU - Mingione, Giuseppe TI - Calderón–Zygmund estimates for measure data problems JO - Comptes Rendus. Mathématique PY - 2007 SP - 437 EP - 442 VL - 344 IS - 7 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.02.005/ DO - 10.1016/j.crma.2007.02.005 LA - en ID - CRMATH_2007__344_7_437_0 ER -
%0 Journal Article %A Mingione, Giuseppe %T Calderón–Zygmund estimates for measure data problems %J Comptes Rendus. Mathématique %D 2007 %P 437-442 %V 344 %N 7 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.02.005/ %R 10.1016/j.crma.2007.02.005 %G en %F CRMATH_2007__344_7_437_0
Mingione, Giuseppe. Calderón–Zygmund estimates for measure data problems. Comptes Rendus. Mathématique, Tome 344 (2007) no. 7, pp. 437-442. doi : 10.1016/j.crma.2007.02.005. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.02.005/
[1] A note on Riesz potentials, Duke Math. J., Volume 42 (1975), pp. 765-778
[2] Sobolev Spaces, Academic Press, New York, 1975
[3] An -theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Volume 22 (1995), pp. 241-273
[4] Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., Volume 87 (1989), pp. 149-169
[5] Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations, Volume 17 (1992), pp. 641-655
[6] Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 13 (1996), pp. 539-551
[7] Proprietà di una famiglia di spazi funzionali, Ann. Scuola Norm. Sup. Pisa (3), Volume 18 (1964), pp. 137-160
[8] Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Volume 28 (1999), pp. 741-808
[9] Uniqueness and maximal regularity for nonlinear elliptic systems of n-Laplace type with measure valued right hand side, J. Reine Angew. Math. (Crelles J.), Volume 520 (2000), pp. 1-35
[10] Inverting the p-harmonic operator, Manuscripta Math., Volume 92 (1997), pp. 249-258
[11] A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with VMO coefficients, J. Funct. Anal., Volume 201 (2003), pp. 457-479
[12] Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa (3), Volume 17 (1963), pp. 43-77
[13] Besov–Morrey spaces: function space theory and applications to non-linear PDE, Trans. Amer. Math. Soc., Volume 355 (2003), pp. 1297-1364
[14] The Calderón–Zygmund theory for elliptic problems with measure data http://www.unipr.it/~mingiu36 (Preprint, September 2006; available at)
[15] Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Volume 15 (1965), pp. 189-258
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