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On the Evans-Krylov theorem


Authors: Luis Caffarelli and Luis Silvestre
Journal: Proc. Amer. Math. Soc. 138 (2010), 263-265
MSC (2000): Primary 35J60
Published electronically: September 4, 2009
MathSciNet review: 2550191
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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 [Enhancements On Off] (What's this?)

  • 1. L. Caffarelli and L. Silvestre.
    The Evans-Krylov theorem for nonlocal fully nonlinear equations.
    Preprint.
  • 2. 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
  • 3. 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, 10.1002/cpa.3160350303
  • 4. 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

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Additional Information

Luis Caffarelli
Affiliation: Department of Mathematics, University of Texas at Austin, 1 University Station – C1200, Austin, Texas 78712-0257
Email: caffarel@math.utexas.edu

Luis Silvestre
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: luis@math.uchicago.edu

DOI: https://doi.org/10.1090/S0002-9939-09-10077-1
Received by editor(s): May 8, 2009
Published electronically: September 4, 2009
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2009 American Mathematical Society