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

作　　者：Siran LI 李思然(School of Mathematical Sciences,IMA-Shanghai&Key Laboratory of Scientific and Engineering Computing(Ministry of Education),Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]School of Mathematical Sciences,IMA-Shanghai&Key Laboratory of Scientific and Engineering Computing(Ministry of Education),Shanghai Jiao Tong University,Shanghai 200240,China

出　　处：《Acta Mathematica Scientia》2022年第4期1427-1452,共26页数学物理学报（B辑英文版）

基　　金：supported by MOE-LSC Project#AF0710029/011。

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[Lr-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.

关 键 词：Gaffney’s inequality differential form Sobolev spaces on manifolds Bochner technique variational approach 

分 类 号：O186.1[理学—数学]