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Spectral Optimization in Unbounded Domains
25 Oct 2017 15:30-17:00
We will discuss recent analytic results on shape optimization for
the lowest eigenvalue of the Robin Laplacian on unbounded domains. The
presentation will be aimed at a broad audience and technical details will be
avoided whenever possible.
The key novel aspect here is the transition from bounded to unbounded
domains. In most, but not in all of the results, that we are going to discuss,
the optimal domain will be the exterior of a ball, under certain geometric
constraints being imposed. A proper choice of these constraints is a task
interesting in its own right. The setting of unbounded domains is somewhat
unusual, because the corresponding Robin Laplacian has non-empty continuous
spectrum, and, in fact, we are optimizing the lowest eigenvalue below
its threshold. As a rule, such spectral optimization results are relatively
easy to formulate, but rather difficult to prove.
In quantum mechanics, the eigenvalue, that we are optimizing, can be
interpreted as the ground-state energy of a Hamiltonian with an attractive
surface interaction placed on the boundary of the domain.
- Place
- Břehová 7, Praha 1, posluchárna č. 115
- Organizer
- FJFI ČVUT v Praze
- Contact person
- Mgr. Jaroslav Bielčík, Ph.D., jaroslav.bielcik@fjfi.cvut.cz
- More information
- https://kolokvium.fjfi.cvut.cz/