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On the negative spectrum of the Robin Laplacian in corner domains

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 Added by Nicolas Popoff
 Publication date 2015
  fields
and research's language is English




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For a bounded corner domain $Omega$, we consider the Robin Laplacian in $Omega$ with large Robin parameter. Exploiting multiscale analysis and a recursive procedure, we have a precise description of the mechanism giving the ground state of the spectrum. It allows also the study of the bottom of the essential spectrum on the associated tangent structures given by cones. Then we obtain the asymptotic behavior of the principal eigenvalue for this singular limit in any dimension, with remainder estimates. The same method works for the Schrodinger operator in $mathbb{R}^n$ with a strong attractive delta-interaction supported on $partialOmega$. Applications to some Erhlings type estimates and the analysis of the critical temperature of some superconductors are also provided.



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