##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Arshak Petrosyan

#### University of Texas

## Obstacle and Stefan type problems with no sign restriction

##### Abstract:

We show how to prove the regularity of free boundaries in these classical problems even if one drops the nonnegativity assumption on the solution (and on its time derivative in the case of Stefan problem). This involves the application of two different kinds of monotonicity formulas: one due to L. Caffarelli to prove the regularity of the solution, and the other due to G. Weiss to classify the free boundary points by their homogeneity properties.

Host: Linda Rothschild

### February 19, 2003

### 1:00 PM

### AP&M CHANGED TO

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