Speaker 

Professor Wolfgang Arendt, University of Ulm, Germany

Abstract

The Dirichlet problem has a long history: Dirchlet tried to solve it by variational methods, Perron found an ingenious weak solution, Wiener obtained a characterization of well posedness in terms of his famous capacity condition, Stampacchia – in the light of the Di Giorgi-Nash result – investigated the Dirichlet problem for general elliptic operators.

We will tell the story of this fascinating problem explaining also some very new results in cases where the maximum principle does not hold. We also explain how the solution of the Dirichlet problem can be used to solve a parabolic problem via semigroup theory.