SMS scnews item created by Daniel Hauer at Wed 5 Jul 2023 1308
Type: Seminar
Distribution: World
Expiry: 7 Jul 2023
Calendar1: 7 Jul 2023 1200-1300
CalLoc1: AGR Carslaw 829
CalTitle1: The Hardy-Davies inequality and spectral lower bounds for elliptic operators
Auth: dhauer@p613m3.pc (assumed)
Informal working Seminar on Analysis and PDEs
The Hardy-Davies inequality and spectral lower bounds for elliptic operators
Jonathan Mui
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.
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