# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Wolfgang
Wendland**, Institut für Angewandte Analysis und Numerische Simulation, University Stuttgart,
will give a public talk (followed by a discussion) on **Fri, Nov. 16, 2012**
at **12:45 o'clock** at **S2 416**
on the topic of
"Elliptic potentials and boundary value problems"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

### Elliptic potentials and boundary value problems

Beginning with the classical boundary potentials and boundary integral equations for the Dirichlet and Neumann problems with the Poisson equation, we give a brief overview of the history of these methods in relation to different assumptions for the domain's boundary and function spaces involved. Then the introduction of energy spaces and coerciveness properties lead to strongly elliptic problems with coercive and strongly elliptic boundary integral equations. These methods can still be applied to the original Gauss problem of potential theory as well as to the Helmholtz equation, the Lam'e equations of linear elasticity, to stationary Stokes and Brinkman equations although the latter are not strongly elliptic but elliptic, and also to time harmonic Maxwell equations. The lecture ends with an outlook to more general regularity properties and to problems on manifolds.