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Archive for Rational Mechanics and Analysis

, Volume 228, Issue 3, pp 923–967 | Cite as

Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions

  • Dongsheng Li
  • Kai Zhang
Article
  • 201 Downloads

Abstract

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 C α, C 1,α and C 2,α regularity. As byproducts, we also prove the A–B–P maximum principle, Harnack inequality, uniqueness and solvability of the equations.

Mathematics Subject Classification

35J25 35B65 35J60 35D40 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina
  2. 2.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina

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