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Lei Zhang

2010-05-20
14:20:00 - 15:20:00

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

For free boundary problems defined in Euclidean spaces, the monotonicity formulas of Alt-Caffarelli-Friedman and Caffarelli-Jerison-Kenig are cornerstones for the regularity theory. I will present the analogs of these results for the Laplace-Beltrami operator on Riemannian manifolds. As an application I will show that the new monotonicity theorems can be employed to prove the Lipschitz continuity for the solutions of a general class of two-phase free boundary problems. This is a joint work with E. Teixeira.