Vector-valued elliptic boundary value problems on rough domains
Marcel Kreuter · OPen Access Repositorium der Universität Ulm (OPARU) (Ulm University) · 2018
In this thesis we study elliptic boundary value problems in the setting of vector-valued functions on arbitrary open and bounded sets. The first part considers Sobolev spaces of vector-valued functions, in particular mapping theorems and their applications. The second part discusses the Dirichlet problem for the Laplacian and a generalized solution which extends Perron's approach for the real-valued case. The third part considers boundary value problems of more general elliptic operators.