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

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• 作者：Charles J.K. Batty^a ; ^{charles.batty@sjc.ox.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Alexander Borichev^b ; ^{alexander.borichev@math.cnrs.fr" class="auth_mail" title="E-mail the corresponding author} ; Yuri Tomilov^c ; ^{ytomilov@impan.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 47D06 ; secondary ; 34D05 ; 34G10 ; 35L05 ; 40E05 ; 44A10
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：270
• 期：3
• 页码：1153-1201
• 全文大小：677 K

文摘

We prove L^p$L^p$-analogues of the classical tauberian theorem of Ingham and Karamata, and its variations giving rates of decay. These results are applied to derive L^p$L^p$-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 L^p$L^p$-rates of decay obtained in this way are best possible under our assumptions.