##### Department of Mathematics,

University of California San Diego

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### Probability/Analysis

## Dennis Bell

#### University of North Florida

## Infinitely Degenerate Hypoelliptic Operators

##### Abstract:

We give a criterion for the hypoellipticity of a class of differentialoperators of Hormander type$$L = 1/2sum_{i = 0}^n X_i^2 + X_0.$$Our criterion is weaker than the usual finite-type Hormander condition and allows for decencies of $L$ of exponential order on hypersurfaces in the ambient space. The methods of proof are probabilistic, being based upon an analysis of the regularity of the diffusion process driven by $L$. These methods are also used to study the Dirichlet problem associated with exponentially degenerate operators $L$.

Host: Bruce Driver

### November 12, 2002

### 12:00 PM

### AP&M 7321

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