Some remarks on the strong maximum principle arising in nonlocal operators

Pascal Autissier and Jerome Coville

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Submission date: 25. Jan. 2008
Pages: 13
published in: Electronic journal of differential equations, 2008 (2008) 66, p. 1-10 
Bibtex
with the following different title: Remarks on the strong maximum principle for nonlocal operators
MSC-Numbers: 47B34, 47B65, 45P05, 35B50
Keywords and phrases: Nonlocal operators, Hausdorff space, Strong maximum principle
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Abstract:
In this note we make some remarks concerning maximum principles holding for nonlocal diffusion operator of the form

where G is a group acting continuously on a Hausdorff space X and . We first investigate the existence of a strong maximum principle in the general situation and then focus on the case of homogeneous spaces. Depending on the topology of the homogenerous space, we give contidions on J and such that achieves a strong maximum principle. We also revisit the classical case of convolution operator on .