Evans-Krylov theorem: Difference between revisions

From nonlocal pde
Jump to navigation Jump to search
imported>Luis
(Created page with "The Evans-Krylov theorem says that if $u$ is a solution to a uniformly elliptic, fully nonlinear, convex or concave, equation \[ F(D^2 u) = 0 \text{ in } B_1,\] then $u \in C^{2,...")
 
(No difference)

Latest revision as of 16:59, 13 May 2012

The Evans-Krylov theorem says that if $u$ is a solution to a uniformly elliptic, fully nonlinear, convex or concave, equation \[ F(D^2 u) = 0 \text{ in } B_1,\] then $u \in C^{2,\alpha}(B_{1/2})$ and there is an estimate \[ \|u\|_{C^{2,\alpha}(B_{1/2})} \leq C \|u\|_{L^\infty(B_1)}, \] where $C$ and $\alpha>0$ depend only on the ellipticity constants and dimension.

This article is a stub. You can help this nonlocal wiki by expanding it.