On Levi Functions

Wolfgang Wendland

Feb. 25, 2010, 10 a.m. T 111

Fundamental solutions to elliptic partial differential operators are explicitly known only in particular cases whereas Levi functions can always be constructed.

In this lecture, the simple case of a second order operator with variable coefficients will be considered and with Levi Functions a system of domain-boundary integral equations for the Dirichlet problem will be obtained. The mapping properties of the corresponding operators will provide the opportunity of employing efficient solution techniques.