Lions? representation theorem and applications

被引：3

作者：

Arendt, W. ^{[1
]}

Chalendar, I. ^{[2
]}

Eymard, R. ^{[2
]}

机构：

[1] Univ Ulm, Inst Appl Anal, Helmholtzstr 18, D-89069 Ulm, Germany

[2] Univ Gustave Eiffel, LAMA, UMR 8050, UPEM,UPEC,CNRS, F-77454 Marne La Vallee, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 522卷 / 02期

关键词：

Lions? representation theorem; Non-autonomous evolution equations; Boundary conditions; Dissipative operators; NONAUTONOMOUS MAXIMAL REGULARITY;

D O I：

10.1016/j.jmaa.2022.126946

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Lions' Representation Theorem (LRT) is a version of the Lax-Milgram Theorem where completeness of one of the spaces is not needed. In this paper, LRT is deduced from an operator-theoretical result on normed spaces, which is of independent interest. As an example, we give a new characterization of dissipativity. The main part of the paper is a theory of derivations, based on LRT, which we develop. Its aim is to establish well-posedness results, not only for evolution in time but also for more general settings in terms of this new notion of derivation. One application concerns non-autonomous evolution equations with a new kind of boundary condition where values at the initial and final time are mixed.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：23

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