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Analysis and PDE

Date:
-
Location:
POT 745
Speaker(s) / Presenter(s):
Ovidiu Savin, Columbia University

Title: Lipschitz regularity and classification of global solutions for certain nonlinear two-phase free boundary problems.

 

Abstract: The two-phase free boundary problem consists in finding a function $u$ that solves a PDE in its positive and negative phases and which has a jump condition discontinuity for the normal derivatives across its zero level set. For the Laplace equation the Lipschitz continuity and the classification of two-phase global solutions was obtained in the 80's by Alt, Caffarelli and Friedman by the use of a monotonicity formula. I will discuss some recent results concerning the Lipschitz continuity of solutions in the context of nonlinear equations which is based on nonvariational techniques. This is a joint work with D. De Silva.