Krzysztof Bogdan, Piotr Knosalla, Łukasz Leżaj, Dominika Pilarczyk
Published 2023-07-04Version 1
We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. As applications, we give the Yaglom limit and entrance law for the corresponding killed isotropic stable L\'{e}vy process and precise large-time asymptotics for solutions of the Cauchy problem in the cone.
Heat kernel of fractional Laplacian in cones
The fractional Laplacian with reflections
Existence and probabilistic representation of the solutions of semilinear parabolic PDEs with fractional Laplacians
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