arXiv:1904.01917 Abstract | arXiv Analytics

arXiv:1904.01917 [math.AP]Abstract References Reviews Resources

On overdetermind problems for a general class of nonlocal operators

Published 2019-04-03Version 1

We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractional Laplacian, relativistic stable operators etc. We consider these problems in bounded domains, exterior domains, and in annular domains and we show that under suitable conditions, the domains and solutions are both radially symmetric. Our method uses both analytic and probabilistic tools.

Categories: math.AP

Keywords: nonlocal operators, general class, overdetermind problems, subordinate brownian motions, probabilistic tools

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