Extensões auto-adjuntas do operador de Schrödinger magnético em domínios com pouca regularidade

• Autor(a) principal: Monteiro, Wagner
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/12954
• topic: Extensões auto-adjuntas; Domínios quase-convexos; Triplas de fronteiras; Equivalência de gauge; Efeito Aharonov-Bohm; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL

We find one parametrization of all self-adjoint extensions of the magnetic Schrödinger operator, in a quasi-convex domain with compact boundary, and magnetic potentials with low regularity. In this parametrization we use boundary-triples, which also gives a new characterization of all self-adjoint extensions of the Laplacian in quasi-convex domains. Then we discuss gauge transformations for such self-adjoint extensions and generalize, for all self-adjoint extensions, a characterization, due to Helffer, of the gauge equivalence of the Dirichlet magnetic operator with the Dirichlet Laplacian. The relation to the Aharonov-Bohm effect, including irregular solenoids, is also discussed. In particular, in case of (bounded) quasi-convex domains it is shown that if some extension is unitarily equivalent (through the multiplication by a smooth unit function) to a realization with zero magnetic potential, then the same occurs for all self-adjoint realizations