A method for obtaining time-periodic L^p estimates

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• 作者：Mads Kyed ; ^{kyed@mathematik.tu-darmstadt.de" class="auth_mail" title="E-mail the corresponding author} ; Jonas Sauer¹ ; ^{jsauer@mathematik.tu-darmstadt.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B10 ; 35B45 ; 35K05
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 January 2017
• 年：2017
• 卷：262
• 期：1
• 页码：633-652
• 全文大小：345 K

文摘

We introduce a method for showing a priori  05d9782" title="Click to view the MathML source">L^p$L^p$ estimates for time-periodic, linear, partial differential equations set in a variety of domains such as the whole space, the half space and bounded domains. The method is generic and can be applied to a wide range of problems. We demonstrate it on the heat equation. The main idea is to replace the time axis with a torus in order to reformulate the problem on a locally compact abelian group and to employ Fourier analysis on this group. As a by-product, maximal 05d9782" title="Click to view the MathML source">L^p$L^p$ regularity for the corresponding initial-value problem follows without   the notion of R$\mathcal{R}$-boundedness. Moreover, we introduce the concept of a time-periodic fundamental solution.