Geodesic
Abstract Green formulas for triples of Hilbert spaces and sesquilinear forms
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 57 (2015), pp. 71-107

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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. 
@article{CMFD_2015_57_a3,
     author = {N. D. Kopachevsky},
     title = {Abstract {Green} formulas for triples of {Hilbert} spaces and sesquilinear forms},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {71--107},
     publisher = {mathdoc},
     volume = {57},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2015_57_a3/}
}
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N. D. Kopachevsky. Abstract Green formulas for triples of Hilbert spaces and sesquilinear forms. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 57 (2015), pp. 71-107. http://geodesic.mathdoc.fr/item/CMFD_2015_57_a3/