6533b7d0fe1ef96bd125b9f1

RESEARCH PRODUCT

A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter

Domenico Angelo La MannaSimone Cito

subject

Control and Optimizationconvex setsBoundary (topology)variaatiolaskenta01 natural sciencesSet (abstract data type)Perimeter0103 physical sciencesquantitative isoperimetric inequalityConvex setBall (mathematics)0101 mathematicsEigenvalues and eigenvectorsMathematicsosittaisdifferentiaaliyhtälötominaisarvot010102 general mathematicsMathematical analysisRegular polygonMathematics::Spectral Theorymatemaattinen optimointiQuantitative isoperimetric inequalityComputational MathematicsHausdorff distanceControl and Systems EngineeringRobin eigenvalue010307 mathematical physicsLaplace operator

description

The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalueλβwith negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer forλβand the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.

yearjournalcountryeditionlanguage
2021-01-01
http://urn.fi/URN:NBN:fi:jyu-202109014751