Boundary regularity for viscosity solutions of fully nonlinear elliptic\n equations

2013/06/27 by Luís Silvestre, Silvestre, Luis, Boyan Sirakov +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1306.6672

Abstract

We provide regularity results at the boundary for continuous viscosity\nsolutions to nonconvex fully nonlinear uniformly elliptic equations and\ninequalities in Euclidian domains. We show that (i) any solution of two sided\ninequalities with Pucci extremal operators is C^1,\α on the boundary;\n(ii) the solution of the Dirichlet problem for fully nonlinear uniformly\nelliptic equations is C^2,\α on the boundary; (iii) corresponding\nasymptotic expansions hold. This is an extension to viscosity solutions of the\nclassical Krylov estimates for smooth solutions.\n

Cited by

• Interior C^2,α regularity for fully nonlinear uniformly elliptic equations in dimension two
• Liouville theorems for fully nonlinear elliptic equations on half spaces

Related

• Boundary Pointwise C^1,α and C^2,α Regularity for Fully Nonlinear Elliptic Equations
• Sharp boundary and global regularity for degenerate fully nonlinear elliptic equations
• Estimates for viscosity solutions of fully nonlinear equations near smooth boundaries
• Partial regularity of solutions of fully nonlinear uniformly elliptic\n equations
• Regularity of viscosity solutions to fully nonlinear elliptic transmission problems