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 $\mathbb{R}^{n-1}$.