Giovedì 29 giugno alle ore 11:00 in aula U5-3014, il Simone Dovetta (Politecnico di Torino) terrà un seminario dal titolo
Singular Limits of Periodic Metric Grids
Abstract:
The talk discusses the asymptotic behaviour of nonlinear Schrodinger ground states on d-dimensional periodic metric grids in the limit for the length of the edges going to zero. After a brief overview of the ground state problems on R^d and on grids, we show that suitable piecewise-affine extensions of such states on grids converge strongly in H^{1}(R^{d}) to the corresponding ground states on R^{d}. As an application of such convergence results, qualitative properties of ground states and multiplicity results for fixed mass critical points of the energy on grids are derived. Moreover, we compare optimal constants in d-dimensional Gagliardo-Nirenberg inequalities on R^d and on grids. For L^2 critical and supercritical powers, we show that the value of such constants on grids is strictly related to that on R^d but, contrary to R^d, constants on grids are not attained.
Tutti gli interessati sono invitati a partecipare!