Science China Mathematics

, Volume 54, Issue 3, pp 457–462 | Cite as

A priori estimates for classical solutions of fully nonlinear elliptic equations

Articles

Abstract

For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n, F and the continuous modulus of D2u.

Keywords

fully nonlinear classical solutions C2,α estimates 

MSC(2000)

35J60 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.College of ScienceXi’an Jiaotong UniversityXi’anChina
  2. 2.Department of MathematicsThe University of IowaIowa CityUSA

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