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On the Evans-Krylov theorem

Author(s): Luis Caffarelli; Luis Silvestre
Journal: Proc. Amer. Math. Soc. 138 (2010), 263-265.
MSC (2000): Primary 35J60
Posted: September 4, 2009
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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:

1.: L. Caffarelli and L. Silvestre.
The Evans-Krylov theorem for nonlocal fully nonlinear equations.
Preprint.
2.: L. A. Caffarelli and X. Cabre.
Fully nonlinear elliptic equations.
Amer. Math. Soc. Colloq. Publ., 43,
American Mathematical Society, Providence, RI, 1995. MR 1351007 (96h:35046)
3.: Lawrence C. Evans.
Classical solutions of fully nonlinear, convex, second-order elliptic equations.
Comm. Pure Appl. Math., 35(3):333-363, 1982. MR 649348 (83g:35038)
4.: N. V. Krylov.
Boundedly inhomogeneous elliptic and parabolic equations.
Izv. Akad. Nauk SSSR Ser. Mat., 46(3):487-523, 670, 1982. MR 661144 (84a:35091)


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