J. L. Lions' problem on maximal regularity

被引：20

作者：

Arendt, Wolfgang ^{[1
]}

Dier, Dominik ^{[1
]}

Fackler, Stephan ^{[1
]}

机构：

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

来源：

ARCHIV DER MATHEMATIK | 2017年 / 109卷 / 01期

关键词：

Sesquilinear forms; Non-autonomous evolution equations; Maximal regularity; SQUARE-ROOT PROBLEM; PSEUDODIFFERENTIAL-OPERATORS; NONAUTONOMOUS FORMS; BOUNDARY-CONDITIONS; ELLIPTIC-OPERATORS; EQUATIONS; SPACES; DOMAINS;

D O I：

10.1007/s00013-017-1031-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It also contains two new results showing the limits of the theory.

引用

页码：59 / 72

页数：14

共 35 条

[1]

Achache M., 2016, ARXIV160700254V1

[2]

[Anonymous], 1962, J. Math. Soc. Japan, DOI 10.2969/jmsj/01420242

[3] Functional calculus, variational methods and Liapunov's theorem [J].

Arendt, W ;

Bu, SQ ;

Haase, M .

ARCHIV DER MATHEMATIK, 2001, 77 (01) :65-75

[4] Maximal regularity for non-autonomous Robin boundary conditions [J].

Arendt, Wolfgang ;

Monniaux, Sylvie .

MATHEMATISCHE NACHRICHTEN, 2016, 289 (11-12) :1325-1340

[5]

Arendt W, 2014, ADV DIFFERENTIAL EQU, V19, P1043

[6]

Arendt W, 2010, ANN SCUOLA NORM-SCI, V9, P523

[7] ON THE RIGHT MULTIPLICATIVE PERTURBATION OF NON-AUTONOMOUS Lp-MAXIMAL REGULARITY [J].

Augner, Bjoern ;

Jacob, Birgit ;

Laasri, Hafida .

JOURNAL OF OPERATOR THEORY, 2015, 74 (02) :391-415

[8] Square roots of elliptic second order divergence operators on strongly Lipschitz domains:: L2 theory [J].

Auscher, P ;

Tchamitchian, P .

JOURNAL D ANALYSE MATHEMATIQUE, 2003, 90 (1) :1-12

[9] The solution of the Kato square root problem for second order elliptic operators on Rn [J].

Auscher, P ;

Hofmann, S ;

Lacey, M ;

McIntosh, A ;

Tchamitchian, P .

ANNALS OF MATHEMATICS, 2002, 156 (02) :633-654

[10] On non-autonomous maximal regularity for elliptic operators in divergence form [J].

Auscher, Pascal ;

Egert, Moritz .

ARCHIV DER MATHEMATIK, 2016, 107 (03) :271-284

← 1 2 3 4 →