Partial regularity of solutions of fully nonlinear, uniformly elliptic equations
Article first published online: 15 MAR 2012
Copyright © 2012 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 65, Issue 8, pages 1169–1184, August 2012
How to Cite
Armstrong, S. N., Silvestre, L. E. and Smart, C. K. (2012), Partial regularity of solutions of fully nonlinear, uniformly elliptic equations. Comm. Pure Appl. Math., 65: 1169–1184. doi: 10.1002/cpa.21394
- Issue published online: 22 MAY 2012
- Article first published online: 15 MAR 2012
- Manuscript Received: MAR 2011
- National Science Foundation Grant. Grant Numbers: DMS-1004645, DMS-1001629, DMS-1004595
- Sloan Foundation
We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is C2,α on the complement of a closed set of Hausdorff dimension at most ϵ less than the dimension. The equation is assumed to be C1, and the constant ϵ > 0 depends only on the dimension and the ellipticity constants. The argument combines the W2,ϵ estimates of Lin with a result of Savin on the C2,α regularity of viscosity solutions that are close to quadratic polynomials. © 2012 Wiley Periodicals, Inc.