Alexandroff–Bakelman–Pucci estimate for singular or degenerate fully nonlinear elliptic equations

Gonzalo Dávila; Patricio Felmer; Alexander Quaas

doi:10.1016/j.crma.2009.09.009

Partial Differential Equations

Alexandroff–Bakelman–Pucci estimate for singular or degenerate fully nonlinear elliptic equations
[Inégalité d'Alexandroff–Bakelman–Pucci pour des équations elliptiques entièrement non linéaires singulières ou dégénérés]

Présenté par : Pierre-Louis Lions

Gonzalo Dávila ¹ ; Patricio Felmer ¹ ; Alexander Quaas ²

¹ Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR2071 CNRS-UChile, Universidad de Chile, Santiago, Chile
² Departamento de Matemática, Universidad Técnica Federico Santa María, Av. Espana 1680, V-110 Valparaiso, Chile

Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1165-1168.

Résumé
Abstract

Nous prouvons l'inégalité classique d'Alexandroff–Bakelman–Pucci pour des équations elliptiques entièrement non linéaires avec des opérateurs singulières ou dégénérés ayant comme modèles ${| p |}^{α} M_{λ, Λ}^{\pm} (X)$ où $M_{λ, Λ}^{\pm}$ sont les opérateurs extremal de Pucci avec des paramètres $0 < λ ⩽ Λ$ et $α > - 1$ .

We prove the classical Alexandroff–Bakelman–Pucci estimate for fully nonlinear elliptic equations involving singular or degenerate operators having as models ${| p |}^{α} M_{λ, Λ}^{\pm} (X)$ , where $M_{λ, Λ}^{\pm}$ are the Pucci extremal operators with parameters $0 < λ ⩽ Λ$ and $α > - 1$ .

Reçu le : 2008-12-23
Accepté le : 2009-09-01
Publié le : 2009-09-24

DOI : 10.1016/j.crma.2009.09.009

Affiliations des auteurs :

Gonzalo Dávila ¹ ; Patricio Felmer ¹ ; Alexander Quaas ²

¹ Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR2071 CNRS-UChile, Universidad de Chile, Santiago, Chile
² Departamento de Matemática, Universidad Técnica Federico Santa María, Av. Espana 1680, V-110 Valparaiso, Chile

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     author = {Gonzalo D\'avila and Patricio Felmer and Alexander Quaas},
     title = {Alexandroff{\textendash}Bakelman{\textendash}Pucci estimate for singular or degenerate fully nonlinear elliptic equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1165--1168},
     publisher = {Elsevier},
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     year = {2009},
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Gonzalo Dávila; Patricio Felmer; Alexander Quaas. Alexandroff–Bakelman–Pucci estimate for singular or degenerate fully nonlinear elliptic equations. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1165-1168. doi : 10.1016/j.crma.2009.09.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.009/

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