In this note, we study the existence of a strong maximum principle for the nonlocal operator
where is a topological group acting continuously on a Hausdorff space and . First we investigate the general situation and derive a pre-maximum principle. Then we restrict our analysis to the case of homogeneous spaces (i.e., ). For such Hausdorff spaces, depending on the topology, we give a condition on such that a strong maximum principle holds for . We also revisit the classical case of the convolution operator (i.e. ).
Submitted January 25, 2008. Published May 1, 2008.
Math Subject Classifications: 35B50, 47G20, 35J60.
Key Words: Nonlocal diffusion operators; maximum principles; Geometric condition.
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| Jérôme Coville |
Max Planck Institute for mathematical science
Inselstrasse 22, D-04103 Leipzig, Germany
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