On maximal regularity for a class of evolutionary equations

详细信息    查看全文

• 作者：Rainer Picard^a ; ^{rainer.picard@tu-dresden.de} ; Sascha Trostorff^a ; ^{sascha.trostorff@tu-dresden.de} ; Marcus Waurick^b ; ^{marcus.waurick@tu-dresden.de}
• 关键词：Maximal regularity ; Evolutionary equations ; Material laws ; Coupled systems
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1368-1381
• 全文大小：362 K
• 卷排序：449

文摘

The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sum of two unbounded operators, showing maximal regularity amounts to establishing that the operator sum considered with its natural domain is already closed. For this we use structural constraints of the coefficients rather than semi-group strategies or sesqui-linear form methods, which would be difficult to come by for our general problem class. Our approach, although limited to the Hilbert space case, complements known strategies for approaching maximal regularity and extends them in a different direction. The abstract findings are illustrated by re-considering some known maximal regularity results within the framework presented.