Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 66, pp. 110.
Remarks on the strong maximum principle for nonlocal operators
Jérôme Coville
Abstract:
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 premaximum
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, D04103 Leipzig, Germany
email: coville@mis.mpg.de 
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