Symmetry of odd solutions to equations with fractional Laplacian
- We 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.
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| Author: | Sidy Moctar DjitteGND, Sven JarohsORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-696007 |
| DOI: | https://doi.org/10.1007/s41808-022-00146-z |
| ISSN: | 2296-9039 |
| Parent Title (English): | Journal of elliptic and parabolic equations |
| Publisher: | Springer International Publishing AG , Orthogonal Editions [2015-[?]] |
| Place of publication: | Cham , Zürich |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2022/02/03 |
| Date of first Publication: | 2022/02/03 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2023/10/12 |
| Tag: | Nonlocal operators; Sign-changing solutions; Symmetries |
| Volume: | 8 |
| Issue: | 1 |
| Page Number: | 22 |
| First Page: | 209 |
| Last Page: | 230 |
| Note: | This work is supported by DAAD and BMBF (Germany) within the project 57385104. |
| Note: | Open Access funding enabled and organized by Projekt DEAL. |
| Note: | Djitte, Sidy Moctar: sidy.m.djitte@aims-senegal.org |
| HeBIS-PPN: | 515067717 |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B06 Symmetries, invariants, etc. |
| 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B50 Maximum principles | |
| 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Sxx Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40] / 35S15 Boundary value problems for pseudodifferential operators | |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
