On the optimization of the Robin eigenvalues in some classes of polygons
Abstract
Given the eigenvalue problem for the Laplacian with Robin boundary conditions, (with β∈\0\ the Robin parameter), we consider a shape minimization problem for a function of the first eigenvalues if β>0 and a shape maximization problem if β<0. Both problems are settled in a suitable class of generalized polygons with an upper bound on the number of sides, under either perimeter or volume constraint.
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