Self-similar solution for fractional Laplacian in cones
Abstract
We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. Furthermore, we give the entrance law from the vertex and the Yaglom limit for the corresponding killed isotropic stable Lévy process and precise large-time asymptotics for solutions of the Cauchy problem in the cone.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Institute of Mathematical Statistics
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202405033299Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1083-6489
DOI
https://doi.org/10.1214/24-EJP1111
Language
English
Published in
Electronic Journal of Probability
Citation
- Bogdan, K., Knosalla, P., Leżaj, Ł., & Pilarczyk, D. (2024). Self-similar solution for fractional Laplacian in cones. Electronic Journal of Probability, 29, Article 54. https://doi.org/10.1214/24-EJP1111
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Additional information about funding
Krzysztof Bogdan was partially supported by the National Science Centre (Poland): grant 2017/27/B/ST1/01339. Łukasz Leżaj was partially supported by the National Science Centre (Poland): grant 2021/41/N/ST1/04139.
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