APS
Speaker: Kshitij Sinha, IIT Bombay
Host: Harsha Hutridurga
Title: Spectral Problems and Fine Properties of Solutions in Periodic Homogenization
Time, day and date: 4:30:00 PM – 5:30:00 PM, Monday, September 28
Venue: Ramanujan Hall
Abstract: In this talk, I will discuss spectral problems for the Laplacian and the Bilaplacian in perforated domains with various boundary conditions, as well as fine properties of solutions to divergence-form elliptic PDEs, in the context of quasi-periodic and almost-periodic homogenization.
First, I will present theoretical results on the asymptotic behaviour of eigenvalues of the Bilaplacian, motivated by a work of Nandakumaran. Next, I will discuss a numerical study of the Neumann eigenvalues of the Laplacian in perforated domains, motivated by a work of Vanninathan. Finally, I will derive doubling inequalities for divergence form elliptic equations with quasi-periodic and almost-periodic coefficients.