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

doi:10.1007/s10473-022-0410-7

Abstract

Abstract: 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 $à la$ Kozono-Yanagisawa [$L^r$-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains, Indiana Univ. Math. J. $\textbf{58}$ (2009), 1853-1920], combined with global computations based on the Bochner technique.

Key words: Gaffney's inequality, differential form, Sobolev spaces on manifolds, Bochner technique, variational approach

CLC Number:

58A10

Siran LI. A NEW PROOF OF GAFFNEY’S INEQUALITY FOR DIFFERENTIAL FORMS ON MANIFOLDS-WITH-BOUNDARY: THE VARIATIONAL APPROACH À LA KOZONO–YANAGISAWA[J].Acta mathematica scientia,Series B, 2022, 42(4): 1427-1452.

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

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