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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 show that if the curve length is kept fixed, the first eigenvalue referring to the fixed-width strip is for any value of the Robin parameter maximized by a circular annulus. Furthermore, we prove that the second eigenvalue in the exterior of a convex domain $Omega$ corresponding to a negative Robin parameter does not exceed the analogous quantity for a disk whose boundary has a curvature larger than or equal to the maximum of that for $partialOmega$.
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
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 spectr
We study Riesz means of the eigenvalues of the Heisenberg Laplacian with Dirichlet boundary conditions on bounded domains. We obtain an inequality with a sharp leading term and an additional lower order term, improving the result of Hanson and Laptev.
We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner openings,
We discuss several geometric conditions guaranteeing the finiteness or the infiniteness of the discrete spectrum for Robin Laplacians on conical domains.