A NEW PROOF OF GAFFNEY'S INEQUALITY FOR DIFFERENTIAL FORMS ON MANIFOLDS-WITH-BOUNDARY: THE VARIATIONAL APPROACH A LA KOZONO-YANAGISAWA

被引：0

作者：

Li, Siran ^{[1
,2
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, IMA Shanghai, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, Key Lab Sci & Engn Comp, Minist Educ, Shanghai 200240, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2022年 / 42卷 / 04期

关键词：

Gaffney's inequality; differential form; Sobolev spaces on manifolds; Bochner technique; variational approach; HODGE THEORY; SPACES;

D O I：

10.1007/s10473-022-0410-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (M, g(0)) be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M, via a variational approach a la Kozono-Yanagisawa [L-r-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains, Indiana Univ. Math. J. 58 (2009), 1853-1920], combined with global computations based on the Bochner technique.

引用

页码：1427 / 1452

页数：26