On the Evans-Krylov theorem
HTML articles powered by AMS MathViewer
- by Luis Caffarelli and Luis Silvestre PDF
- Proc. Amer. Math. Soc. 138 (2010), 263-265 Request permission
Abstract:
We provide a short proof of the $C^{2,\alpha }$ interior estimate for convex fully nonlinear elliptic equations. This result was originally proved by L. C. Evans and N. Krylov. Our proof is based on the ideas from our work on integro-differential equations.References
- L. Caffarelli and L. Silvestre. The Evans-Krylov theorem for nonlocal fully nonlinear equations. Preprint.
- Luis A. Caffarelli and Xavier Cabré, Fully nonlinear elliptic equations, American Mathematical Society Colloquium Publications, vol. 43, American Mathematical Society, Providence, RI, 1995. MR 1351007, DOI 10.1090/coll/043
- Lawrence C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 35 (1982), no. 3, 333–363. MR 649348, DOI 10.1002/cpa.3160350303
- N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 3, 487–523, 670 (Russian). MR 661144
Additional Information
- Luis Caffarelli
- Affiliation: Department of Mathematics, University of Texas at Austin, 1 University Station – C1200, Austin, Texas 78712-0257
- MR Author ID: 44175
- Email: caffarel@math.utexas.edu
- Luis Silvestre
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 757280
- Email: luis@math.uchicago.edu
- Received by editor(s): May 8, 2009
- Published electronically: September 4, 2009
- Communicated by: Matthew J. Gursky
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 263-265
- MSC (2000): Primary 35J60
- DOI: https://doi.org/10.1090/S0002-9939-09-10077-1
- MathSciNet review: 2550191