##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Luis Silvestre

#### Courant Institute \\ New York University

## Fully nonlinear integro-differential equations

##### Abstract:

We study nonlinear integro-differential equations. Typical examples are the ones that arise from stochastic control problems with discontinuous Levy processes. We can think of these as nonlinear equations of fractional order. Indeed, second order elliptic PDEs are limit cases for integro-differential equations. Our aim is to extend the theory of fully nonlinear elliptic equations to this class of equations. We are able to obtain a result analogous to the Alexandroff estimate, Harnack inequality and $C^{1,\alpha}$ regularity. As the order of the equation approaches two, in the limit our estimates become the usual regularity estimates for second order elliptic pdes. This is a joint work with Luis Caffarelli.

Host: Bo Li

### November 20, 2007

### 12:00 PM

### AP&M 6402

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