Author:
Krejčiřík David,Lotoreichik Vladimir,Vu Tuyen
Abstract
AbstractWe consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter.
Funder
Grantová Agentura České Republiky
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
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