A short proof of the $C^{0,\alpha}$--regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2010

A short proof of the $C^{0,\alpha}$--regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications

Résumé

Recently I.~Capuzzo Dolcetta, F.~Leoni and A.~Porretta obtain a very surprising regularity result for fully nonlinear, superquadratic, elliptic equations by showing that viscosity subsolutions of such equations are locally Hölder continuous, and even globally if the boundary of the domain is regular enough. The aim of this paper is to provide a simplified proof of their results, together with an interpretation of the regularity phenomena, some extensions and various applications.
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Dates et versions

hal-00375575 , version 1 (15-04-2009)

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Guy Barles. A short proof of the $C^{0,\alpha}$--regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications. Nonlinear Analysis: Theory, Methods and Applications, 2010, 73 (1), pp.31-47. ⟨hal-00375575⟩
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