This article is cited in 12 papers

Abstract Green formulas for triples of Hilbert spaces and sesquilinear forms

N. D. Kopachevsky

Crimea Federal University, Simferopol'

Abstract: In this paper, under several general assumptions, we deduce an abstract Green formula for a triple of Hilbert spaces and an (abstract) trace operator and a similar formula corresponding to sesquilinear forms. We establish existence conditions for the abstract Green formula for mixed boundary-value problems. As the main application, we deduce generalized Green formulas for the Laplace operator applied to boundary-value problems in Lipschitz domains.

UDC: 517.95+517.98

 English version: Journal of Mathematical Sciences, 2017, 225:2, 226–264