IISER MOHALI

Abstract: In this talk, I am going to talk about an eigenvalue optimisation problem over a family of doubly connected domains U:=D∖Ω in R^2 where ∂D, one boundary component, is a circle while the other component, ∂Ω, enjoys a dihedral symmetry. The Boundary Value Problem under consideration is Δu=0 on D∖Ω, u=0 on ∂D and ∂u/∂n=σu on ∂Ω. We study the behaviour of the first nonzero eigenvalue of this problem as the domain Ω rotates about its own center by an angle θ in the anticlockwise direction. We also investigate if there is any symmetry, monotonicity in the behaviour of the eigenvalue as a function of θ, and try to find global maximisers and global minimisers of the eigenvalue with respect to θ. This is based on a joint work with Sagar Basak, Ravi Prakash and Sheela Verma.