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Title
Solutions of fully nonlinear equations with patches of zero gradient: existence, regularity and convexity of level curves

Abstract
In this talk (a joint work with Luis Caffarelli), we are going to report on the construction of viscosity solutions (in the Crandall-Lions sense) of fully nonlinear equations of the form $F(D^2 u,x) = g(x,u)$ on $\{|\nabla u| \ne 0$. By an appropiate use of the Alexandroff-Backelmann technique, we prove existence, regularity and, in two dimensions, for $F=\Delta$, $g = cu$ ($c>0$) and constant boundary conditions on a convex domain, we prove that there is only one convex patch.

Speaker(s)
Jorge Salazar, CMAF, Universidade de Lisboa, Portugal

Date
May 05, 2000

Time

Room
Room 5.5

 
     
 

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