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

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

2009-04-15

arxiv.org/abs/0904.2309v1

Nonlinear Analysis: Theory, Methods and Applications 73, 1 (2010) 31-47

Mathematics

Analysis of PDEs

Scientific paper

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 H\"older 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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