L^p-Tauberian theorems and L^p-rates for energy decay

Author: 

Batty, C
Borichev, A
Tomilov, Y

Publication Date: 

28 December 2015

Journal: 

Journal of Functional Analysis

Last Updated: 

2020-10-29T14:26:01.537+00:00

Issue: 

3

Volume: 

270

DOI: 

10.1016/j.jfa.2015.12.003

page: 

1153-1201

abstract: 

We prove Lp-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive Lp-decay of operator families arising in the study of the decay of energy for damped wave equations and local energy for wave equations in exterior domains. By constructing some examples of critical behaviour we show that the Lp-rates of decay obtained in this way are best possible under our assumptions.

Symplectic id: 

580079

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article