This paper deals with the eigenvalue problem for the operator L=-δ-x{dot operator}∇ 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.
Brandolini B., Chiacchio F., Henrot A., Trombetti C. (2015). Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift. JOURNAL OF DIFFERENTIAL EQUATIONS, 259(2), 708-727 [10.1016/j.jde.2015.02.028].
Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift
Brandolini B.
;
2015-01-01
Abstract
This paper deals with the eigenvalue problem for the operator L=-δ-x{dot operator}∇ 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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