Abstract
AbstractWe present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has a fixed sign on one side, then it will be symmetric in the perpendicular direction. Moreover, the solution will be monotonic in the part where it is of fixed sign. In addition, we present also a class of examples in which our result can be applied.
Funder
Johann Wolfgang Goethe-Universität, Frankfurt am Main
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Numerical Analysis,Analysis
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