##### Department of Mathematics,

University of California San Diego

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### Math 196/296 - Student Colloquium

## Peter Ebenfelt

#### UCSD

## The classical Dirichlet problem with rational data

##### Abstract:

The Dirichlet problem (DP) for the Laplace operator can be used to model a number of different physical situations. For instance, if the surface of a ball is kept at a given constant temperature f, then the steady state temperature inside the ball is given by the solution of the Dirichlet problem in the ball with data f on the sphere. A curious fact is that the solution of the DP with rational data on the unit disk in the plane is rational, whereas the corresponding statement is not true in 3-space (or in any dimension greater than or equal to 3 for that matter). This can be explained by quite elementary methods. Refreshments will be served.

Host:

### November 5, 2003

### 11:00 AM

### AP&M 2402

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