Symmetry Breaking for Ground States of Biharmonic Nonlinear Schrödinger Equations


Event details

Date 05.11.2021 14:1515:15  
Speaker Prof. Tobias Weth (Goethe-Universität Frankfurt am Main, Germany)
Location Online
Category Conferences - Seminars
Event Language English

We consider ground states solutions, suitably defined as energy minimizers, of a class of semilinear biharmonic (fourth-order) Schrödinger equations. 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 symmetry breaking result for ground state solutions, which is in striking contrast to the well-known results of radial symmetry for ground states of classical second-order nonlinear Schrödinger equations. We also discuss symmetry breaking for a minimization problem with constrained mass and for a related problem on the unit ball subject to Dirichlet boundary conditions.

This is joint work with Enno Lenzmann (Universität Basel).

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  • B. Buffoni

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