Type: Seminar

Distribution: World

Expiry: 7 Jul 2023

CalTitle1: The Hardy-Davies inequality and spectral lower bounds for elliptic operators

Auth: dhauer@p613m3.pc (assumed)

In this informal PDE seminar, I introduce the classical Hardy inequality and a generalisation due to E.B. Davies.

Following the results in Davies' influential 1989 monograph Heat kernels and spectral theory, we will see that

the latter inequality can be used to obtain lower bounds for the principal eigenvalue of elliptic operators

acting on \(L^2(\Omega)\) under no regularity assumptions on the domain \(\Omega\).

I will also comment on analogous results for the principal eigenvalue of the p-Laplacian.

Following the results in Davies' influential 1989 monograph Heat kernels and spectral theory, we will see that

the latter inequality can be used to obtain lower bounds for the principal eigenvalue of elliptic operators

acting on \(L^2(\Omega)\) under no regularity assumptions on the domain \(\Omega\).

I will also comment on analogous results for the principal eigenvalue of the p-Laplacian.