Journal article
A priori estimates for classical solutions of fully nonlinear elliptic equations
Science China. Mathematics, Vol.54(3), pp.457-462
03/2011
DOI: 10.1007/s11425-010-4092-6
Abstract
For the fully nonlinear uniformly elliptic equation F(D
2
u) = 0, it is well known that the viscosity solutions are C
2,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 C
1,β
a.e. for any 0 < β < 1. We will prove that the classical solutions u are C
2,α
. Moreover, the C
2,α
norm of u depends on n, F and the continuous modulus of D
2
u.
Details
- Title: Subtitle
- A priori estimates for classical solutions of fully nonlinear elliptic equations
- Creators
- Yi Cao - College of Science Xi’an Jiaotong University Xi’an 710049 ChinaDongSheng Li - College of Science Xi’an Jiaotong University Xi’an 710049 ChinaLiHe Wang - Department of Mathematics The University of Iowa Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Science China. Mathematics, Vol.54(3), pp.457-462
- Publisher
- SP Science China Press
- DOI
- 10.1007/s11425-010-4092-6
- ISSN
- 1674-7283
- eISSN
- 1869-1862
- Language
- English
- Date published
- 03/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984083238202771
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