Fourier extension estimates for symmetric functions and applications to nonlinear Helmholtz equations
- We establish weighted Lp-Fourier extension estimates for O(N−k)×O(k)-invariant functions defined on the unit sphere SN−1, allowing for exponents p below the Stein–Tomas critical exponent 2(N+1)/N−1. Moreover, in the more general setting of an arbitrary closed subgroup G⊂O(N) and G-invariant functions, we study the implications of weighted Fourier extension estimates with regard to boundedness and nonvanishing properties of the corresponding weighted Helmholtz resolvent operator. Finally, we use these properties to derive new existence results for G-invariant solutions to the nonlinear Helmholtz equation −Δu−u = Q(x)|u|p−2u,u∈W2,p(RN), where Q is a nonnegative bounded and G-invariant weight function.
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| Author: | Tobias WethORCiDGND, Tolga YeşilGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-638052 |
| DOI: | https://doi.org/10.1007/s10231-021-01086-6 |
| ISSN: | 1618-1891 |
| Parent Title (Italian): | Annali di matematica pura ed applicata |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg [u.a.] |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2021/03/31 |
| Date of first Publication: | 2021/03/31 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2022/09/16 |
| Volume: | 200.2021 |
| Issue: | 6 |
| Page Number: | 32 |
| First Page: | 2423 |
| Last Page: | 2454 |
| Note: | Open Access funding enabled and organized by Projekt DEAL. |
| Note: | T. Weth and T. Yeşil are supported by the German Science Foundation (DFG) within the project WE-2821/5-2. |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
