Symmetry breaking for ground states of biharmonic NLS via Fourier extension estimates
- We consider ground state solutions u ∈ H2(RN) of biharmonic (fourth-order) nonlinear Schrodinger equations of the form ¨2u + 2au + bu − |u| p−2u = 0 in RN with positive constants a, b > 0 and exponents 2 < p < 2∗, where 2∗ = 2N N−4 if N > 4 and 2∗ = ∞ if N ≤ 4. By exploiting a connection to the adjoint Stein–Tomas inequality on the unit sphere and by using trial functions due to Knapp, we prove a general symmetry breaking result by showing that all ground states u ∈ H2(RN) in dimension N ≥ 2 fail to be radially symmetric for all exponents 2 < p < 2N+2 N−1 in a suitable regime of a, b > 0. As applications of our main result, we also prove symmetry breaking for a minimization problem with constrained L2-mass and for a related problem on the unit ball in RN subject to Dirichlet boundary conditions.
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| Author: | Enno LenzmannORCiDGND, Tobias WethORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-841077 |
| DOI: | https://doi.org/10.1007/s11854-023-0311-2 |
| ISSN: | 1565-8538 |
| ArXiv Id: | http://arxiv.org/abs/2110.10782 |
| Parent Title (English): | Journal d’Analyse Mathématique |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/12/12 |
| Date of first Publication: | 2023/12/12 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2024/07/16 |
| Volume: | 152.2023 |
| Page Number: | 24 |
| First Page: | 777 |
| Last Page: | 800 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
