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Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

Antoine HenrotBarbara BrandoliniCristina TrombettiFrancesco Chiacchio

subject

Pure mathematicsMinimization of eigenvalueStructure (category theory)01 natural sciencesMeasure (mathematics)symbols.namesakeMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Weighted Sobolev spaces0101 mathematicsComputingMilieux_MISCELLANEOUSEigenvalues and eigenvectorsMathematicsApplied MathematicsOperator (physics)010102 general mathematicsMinimization problemMathematics::Spectral Theory010101 applied mathematicsDirichlet laplacianDirichlet boundary conditionDirichlet–Laplacian with a driftsymbolsAnalysisAnalysis of PDEs (math.AP)

description

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 λ k 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 problem min ⁡ { λ k ( Ω ) : Ω quasi-open set , ∫ Ω e | x | 2 / 2 d x ≤ c } has a solution.

yearjournalcountryeditionlanguage
2015-07-01
10.1016/j.jde.2015.02.028http://hdl.handle.net/11588/611314