Abstract
This paper deals with the eigenvalue problem for the operator L=−Δ−x⋅∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λk of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c>0 and k∈N the following minimization problemmin{λk(Ω):Ωquasi-openset,∫Ωe|x|2/2dx≤c} has a solution.
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