Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue
Ilias Ftouhi
Abstract
We prove that among all doubly connected domains of ℝ n of the form B 1 \ B ̅ 2 , where B 1 and B 2 are open balls of fixed radii such that B ̅ 2 ⊂ B 1 , the first nonzero Steklov eigenvalue achieves its maximal value uniquely when the balls are concentric. Furthermore, we show that the ideas of our proof also apply to a mixed boundary conditions eigenvalue problem found in literature.
Topics & Concepts
Eigenvalues and eigenvectorsMathematicsObstacleBoundary (topology)Boundary value problemCombinatoricsMathematical analysisPure mathematicsPhysicsQuantum mechanicsLawPolitical scienceAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsAdvanced Numerical Methods in Computational Mathematics