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On the Dirichlet Problem for Pseudodifferential Operators Generating Feller Semigroups

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
137
Issue
1
Identifiers
DOI: 10.1006/jfan.1996.0039

Abstract

Abstract For pseudo-differential operators generating symmetric Feller semigroups we discuss several approaches to the Dirichlet problem and show that under suitable regularity assumptions the solutions obtained by different methods do all coincide. In particular, we give a reasonable analytic interpretation to a probabilistic approach to the Dirichlet problem.

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