I will discuss the existence and orbital stability of standing-wave solutions (i.e., with a specific time-dependence) with minimal energy (so-called ground states) to a non-linear Schrödinger equation where the L² norm is prescribed. I will focus on the simpler case where the energy is bounded below and show a novel approach that simplifies the proof.  Zoom Meeting: Link  

We study the effect of total variation regularization on PDE-constrained optimization problems, where the control input functions may only attain finitely many integer values. The regularization helps to avoid undesirable effects such as chattering behavior. In particular, the weak-* compactness of the feasible set in the space of functions of bounded variation allows to derive…