Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions

By Dongsheng Li, Kai Zhang. Archive for Rational Mechanics and Analysis, 2017

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In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise Cα, C1,α and C2,α regularity. As byproducts, we also prove the A–B–P maximum principle, Harnack inequality, uniqueness and solvability of the equations.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/0154f82a76332b62528210ca934b59b44375e227