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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.
We discuss several geometric conditions guaranteeing the finiteness or the infiniteness of the discrete spectrum for Robin Laplacians on conical domains.
In this paper we deal with spectral optimization for the Robin Laplacian on a family of planar domains admitting parallel coordinates, namely a fixed-width strip built over a smooth closed curve and the exterior of a convex set with a smooth boundary
We consider the magnetic Robin Laplacian with a negative boundary parameter. Among a certain class of domains, we prove that the disk maximizes the ground state energy under the fixed perimeter constraint provided that the magnetic field is of modera
Let $Omegasubsetmathbb{R}^ u$, $ uge 2$, be a $C^{1,1}$ domain whose boundary $partialOmega$ is either compact or behaves suitably at infinity. For $pin(1,infty)$ and $alpha>0$, define [ Lambda(Omega,p,alpha):=inf_{substack{uin W^{1,p}(Omega) u otequ
Let $Omega$ be a curvilinear polygon and $Q^gamma_{Omega}$ be the Laplacian in $L^2(Omega)$, $Q^gamma_{Omega}psi=-Delta psi$, with the Robin boundary condition $partial_ u psi=gamma psi$, where $partial_ u$ is the outer normal derivative and $gamma>0