Gagliardo-Nirenberg Inequalities for Horizontal Vector Fields in the Engel Group and in the Seven-Dimensional Quaternionic Heisenberg Group

被引：6

作者：

Baldi, Annalisa ^{[1
]}

Franchi, Bruno ^{[1
]}

Tripaldi, Francesca ^{[2
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Bologna, Italy

[2] Kings Coll London, Dept Math, London, England

来源：

GEOMETRIC METHODS IN PDE'S | 2015年 / 13卷

关键词：

Differential forms; Div-curl systems; Engel group; Gagliardo-Nirenberg inequalities; Quaternionic Heisenberg groups; NILPOTENT LIE-GROUPS; CARNOT GROUPS; DIV-CURL; COMPENSATED COMPACTNESS; SOBOLEV INEQUALITIES; DIFFERENTIAL FORMS; SYSTEMS; EQUATIONS; OPERATORS; SPACES;

D O I：

10.1007/978-3-319-02666-4_16

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently, Bourgain and Brezis and Lanzani and Stein considered a class of div-curl inequalities in de Rham's complex. In this note we prove the natural counterpart of these inequalities for horizontal vector fields in the Engel group and in the seven-dimensional quaternionic Heisenberg group.

引用

页码：287 / 312

页数：26

共 39 条

[1] [Anonymous], 1985, PROGR MATH
[2] [Anonymous], 1982, Mathematical Notes, DOI DOI 10.1515/9780691222455
[3] Baldi A., ARXIV150605904
[4] Baldi A., ACTA MATH S IN PRESS
[5] Compensated compactness in the contact complex of Heisenberg groups
Baldi, Annalisa
Franchi, Bruno
Tesi, Maria Carla
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (01) : 133 - 185
[6] Baldi A, 2015, ADV NONLINEAR STUD, V15, P333
[7] Sharp a priori estimates for div-curl systems in Heisenberg groups
Baldi, Annalisa
Franchi, Bruno
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (10) : 2388 - 2419
[8] Compensated compactness for differential forms in Carnot groups and applications
Baldi, Annalisa
Franchi, Bruno
Tchou, Nicoletta
Tesi, Maria Carla
[J]. ADVANCES IN MATHEMATICS, 2010, 223 (05) : 1555 - 1607
[9] Baldi A, 2009, J EUR MATH SOC, V11, P777
[10] Baldi Annalisa, 2012, B UNIONE MAT ITAL, V9, P337

← 1 2 3 4 →