TY  - JOUR
A1  - Lenzmann, Enno
A1  - Weth, Tobias
T1  - Symmetry breaking for ground states of biharmonic NLS via Fourier extension estimates
T2  - Journal d’Analyse Mathématique
N2  - 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.
Y1  - 2023
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/84107
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-841077
SN  - 1565-8538
VL  - 152
SP  - 777
EP  - 800
PB  - Springer
CY  - Berlin ; Heidelberg
ER  -