Published Paper

Inserted: 15 apr 2024
Last Updated: 1 sep 2025

Journal: Springer INdAM Series
Volume: 64
Pages: 25
Year: 2025
Doi: 10.1007/978-981-96-3584-9_12

Abstract:

We discuss the problem of establishing the existence of the Ground States for the subcritical focusing Nonlinear Schr\"odinger energy on a domain made of a line and a plane intersecting at a point. The problem is physically motivated by the experimental realization of hybrid traps for Bose-Einstein Condensates, that are able to concentrate the system on structures close to the domain we consider. In fact, such a domain approximates the trap as the temperature approaches the absolute zero. The spirit of the paper is mainly pedagogical, so we focus on the formulation of the problem and on the explanation of the result, giving references for the technical points and for the proofs.