Optimal design problems for Schrödinger operators with noncompact resolvents

2015/01/31 by Guy Bouchitté, Bouchitté, Guy, Giuseppe Buttazzo +1
Engineering · Mathematics · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math.AP #msc:35J10 #msc:35P15 #msc:49J45 #msc:49R05 #msc:58C40

paper · pdf · doi:10.48550/arxiv.1502.00091

8 pages, 0 figures

arxiv created 2015/01/31 · arxiv updated 2015/02/03

Abstract

We consider optimization problems for cost functionals which depend on the negative spectrum of Schrödinger operators of the form -Δ+V(x), where V is a potential, with prescribed compact support, which has to be determined. Under suitable assumptions the existence of an optimal potential is shown. This can be applied to interesting cases such as costs functions involving finitely many negative eigenvalues.

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