Comptes Rendus
no. 15-16
Partial Differential Equations
A surprising linear type estimate for nonlinear elliptic equations
[Une estimation de type linéaire surprenante pour des équations elliptiques non linéaires]

Présenté par : Haïm Brezis

Tuomo Kuusi1 ; Giuseppe Mingione2
1 Aalto University, Institute of Mathematics, PO Box 11100, 00076 Aalto, Finland
2 Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/a, Campus, 43100 Parma, Italy
Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 889-892.

Des bornes ponctuelles par potentiels de Riesz semblables à celles disponibles pour lʼéquation de Poisson sont valables pour des équations du type du p-laplacien.

Pointwise gradient bounds via Riesz potentials, like those available for the Poisson equation, actually hold for p-Laplacian type equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.025
Tuomo Kuusi 1 ; Giuseppe Mingione 2

1 Aalto University, Institute of Mathematics, PO Box 11100, 00076 Aalto, Finland
2 Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/a, Campus, 43100 Parma, Italy 
@article{CRMATH_2011__349_15-16_889_0,
     author = {Tuomo Kuusi and Giuseppe Mingione},
     title = {A surprising linear type estimate for nonlinear elliptic equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {889--892},
     publisher = {Elsevier},
     volume = {349},
     number = {15-16},
     year = {2011},
     doi = {10.1016/j.crma.2011.07.025},
     language = {en},
}
TY  - JOUR
AU  - Tuomo Kuusi
AU  - Giuseppe Mingione
TI  - A surprising linear type estimate for nonlinear elliptic equations
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 889
EP  - 892
VL  - 349
IS  - 15-16
PB  - Elsevier
DO  - 10.1016/j.crma.2011.07.025
LA  - en
ID  - CRMATH_2011__349_15-16_889_0
ER  - 
%0 Journal Article
%A Tuomo Kuusi
%A Giuseppe Mingione
%T A surprising linear type estimate for nonlinear elliptic equations
%J Comptes Rendus. Mathématique
%D 2011
%P 889-892
%V 349
%N 15-16
%I Elsevier
%R 10.1016/j.crma.2011.07.025
%G en
%F CRMATH_2011__349_15-16_889_0
Tuomo Kuusi; Giuseppe Mingione. A surprising linear type estimate for nonlinear elliptic equations. Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 889-892. doi : 10.1016/j.crma.2011.07.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.07.025/

[1] L. Boccardo; T. Gallouët Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., Volume 87 (1989), pp. 149-169

[2] L. Boccardo; T. Gallouët Nonlinear elliptic equations with right-hand side measures, Comm. Partial Differential Equations, Volume 17 (1992), pp. 641-655

[3] E. DiBenedetto; J.J. Manfredi On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems, Amer. J. Math., Volume 115 (1993), pp. 1107-1134

[4] F. Duzaar; G. Mingione Gradient estimates via non-linear potentials, Amer. J. Math., Volume 133 (2011), pp. 1093-1149

[5] F. Duzaar; G. Mingione Gradient estimates via linear and nonlinear potentials, J. Funct. Anal., Volume 259 (2010), pp. 2961-2998

[6] T. Iwaniec Projections onto gradient fields and Lp-estimates for degenerated elliptic operators, Studia Math., Volume 75 (1983), pp. 293-312

[7] T. Kilpeläinen; J. Malý Degenerate elliptic equations with measure data and nonlinear potentials, Ann. Sc. Norm. Super. Pisa Cl. Sci. (IV), Volume 19 (1992), pp. 591-613

[8] T. Kilpeläinen; J. Malý The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math., Volume 172 (1994), pp. 137-161

[9] R. Korte; T. Kuusi A note on the Wolff potential estimate for solutions to elliptic equations involving measures, Adv. Calc. Var., Volume 3 (2010), pp. 99-113

[10] T. Kuusi, G. Mingione, Linear potentials in nonlinear potential theory, submitted for publication.

[11] G. Mingione Gradient estimates below the duality exponent, Math. Ann., Volume 346 (2010), pp. 571-627

[12] G. Mingione Gradient potential estimates, J. Eur. Math. Soc., Volume 13 (2011), pp. 459-486

[13] N.C. Phuc; I.E. Verbitsky Quasilinear and Hessian equations of Lane–Emden type, Ann. of Math. (II), Volume 168 (2008), pp. 859-914

[14] N.S. Trudinger; X.J. Wang On the weak continuity of elliptic operators and applications to potential theory, Amer. J. Math., Volume 124 (2002), pp. 369-410

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Calderón–Zygmund estimates for measure data problems

Giuseppe Mingione

C. R. Math (2007)