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Abstract Green formulas for triples of Hilbert spaces and sesquilinear forms. (English. Russian original) Zbl 06816225

J. Math. Sci., New York 225, No. 2, 226-264 (2017); translation from Sovrem. Mat., Fundam. Napravl. 57, 71-107 (2015).
Summary: 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.

MSC:

47-XX Operator theory
34-XX Ordinary differential equations
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