Partial regularity of solutions of fully nonlinear,uniformly elliptic equations |
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| Authors: | Scott N. Armstrong Luis E. Silvestre Charles K. Smart |
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| Affiliation: | 1. Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL 60637;2. Courant Institute, 251 Mercer St., Room 1414, New York, NY 10012 |
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| Abstract: | 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 ? less than the dimension. The equation is assumed to be C1, and the constant ? > 0 depends only on the dimension and the ellipticity constants. The argument combines the W2,? 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. |
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