On a Boundary-Value Problem for Pseudo-Differential Operators and its Relation to Jump Processes

Abstract

We show the solvability of Dirichlet and Neumann boundary-value problems in $L_p({\mathbb{R}}_{+}^n)$ for an operator $A$ of some special type. In case $p=2$ it is possible to give another description of the trace of the domain of $A$ on ${\mathbb{R}}^{n-1}$.