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Communications in Partial Differential Equations

Volume 30, 2005 - Issue 8
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Original Articles

Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order

Richard F. Bass Department of Mathematics , University of Connecticut , Storrs, Connecticut, USA Correspondencebass@math.uconn.edu
&
Moritz Kassmann Department of Mathematics , University of Connecticut , Storrs, Connecticut, USA ; Institut für Angewandte Mathematik , Universität Bonn , Bonn, Germany
Pages 1249-1259
Received 30 Apr 2004
Accepted 19 Jul 2005
Published online: 01 Sep 2006
 
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Original Articles

Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order

ABSTRACT

ABSTRACT

We consider a class of integrodifferential operators and their corresponding harmonic functions. Under mild assumptions on the family of jump measures we prove a priori estimates and establish Hölder continuity of bounded functions that are harmonic in a domain.

Mathematics Subject Classification:

45K0531B0535B6560J75

Acknowledgment

Research partially supported by NSF grant DMS-0244737.

 

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