Wednesday, May 22, 2013

1305.4902 (R. Bedoya et al.)

Complex $Γ$-convergence and magnetic Dirichlet Laplacian in bounded
thin tubes

R. Bedoya, C. R. de Oliveira, A. A. Verri
The resolvent convergence of self-adjoint operators via the technique of $\Gamma$-convergence of quadratic forms is adapted to incorporate complex Hilbert spaces. As an application, we find effective operators to the Dirichlet Laplacian with mag- netic fields in very thin bounded tubular regions in space built along smooth closed curves; the convergence is in the norm resolvent sense as the cross sections of the tubes go uniformly to zero.
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