Gradient and Hölder estimates for positive solutions of Pucci type equations

Italo Capuzzo Dolcetta; Antonio Vitolo

doi:10.1016/j.crma.2008.03.004

Partial Differential Equations

Gradient and Hölder estimates for positive solutions of Pucci type equations
[Estimations Hölder et du gradient pour les solutions non négatives des équations de Pucci]

Présenté par : Louis Nirenberg

Italo Capuzzo Dolcetta ¹ ; Antonio Vitolo ²

¹ Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy
² Dipartimento di Matematica e Informatica, Università di Salerno, P. Grahamstown, 84084 Fisciano (SA), Italy

Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 527-532.

Résumé
Abstract

Le but de cette Note est de donner des estimations pour les solutions de viscosité non négatives d'une classe d'équations complètement non linéaires comprenante les équations extrémales de Pucci, en généralisant ainsi des résultats récents dues à Y.Y. Li et L. Nirenberg.

We present some estimates for positive viscosity solutions of a class of fully non-linear elliptic equations including the extremal Pucci equations, generalizing some results for linear equations recently established by Y.Y. Li and L. Nirenberg.

Reçu le : 2007-11-29
Accepté le : 2008-02-28
Publié le : 2008-04-21

DOI : 10.1016/j.crma.2008.03.004

Affiliations des auteurs :

Italo Capuzzo Dolcetta ¹ ; Antonio Vitolo ²

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     author = {Italo Capuzzo Dolcetta and Antonio Vitolo},
     title = {Gradient and {H\"older} estimates for positive solutions of {Pucci} type equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {527--532},
     publisher = {Elsevier},
     volume = {346},
     number = {9-10},
     year = {2008},
     doi = {10.1016/j.crma.2008.03.004},
     language = {en},
}

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Italo Capuzzo Dolcetta; Antonio Vitolo. Gradient and Hölder estimates for positive solutions of Pucci type equations. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 527-532. doi : 10.1016/j.crma.2008.03.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.004/

Bibliographie
Cité par

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[2] L.A. Caffarelli Interior a priori estimates for solutions of fully nonlinear equations, Ann. of Math., Volume 130 (1989), pp. 189-213

[3] L.A. Caffarelli; X. Cabrè Fully Nonlinear Elliptic Equations, American Mathematical Society Colloquium Publications, vol. 43, American Mathematical Society, Providence, RI, 1995

[4] M.G. Crandall; H. Ishii; P.L. Lions User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., Volume 27 (1992) no. 1, pp. 1-67

[5] L.C. Evans Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math., Volume 25 (1982), pp. 333-363

[6] D. Gilbarg; N.S. Trudinger Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224, Springer-Verlag, Berlin, New York, 1983

[7] H. Ishii; P.L. Lions Viscosity solutions of fully nonlinear second order elliptic partial differential equations, J. Differential Equations, Volume 83 (1990), pp. 26-78

[8] Y.Y. Li; L. Nirenberg Generalization of a well-known inequality, Progress in Nonlinear Differential Equations and Their Applications, vol. 66, 2005, pp. 365-370

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