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.
Citation:
N. D. Kopachevsky, “Abstract Green formulas for triples of Hilbert spaces and sesquilinear forms”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 57, PFUR, M., 2015, 71–107; Journal of Mathematical Sciences, 225:2 (2017), 226–264
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N. D. Kopachevskii, A. R. Yakubova, “O nekotorykh zadachakh, porozhdennykh polutoralineinoi formoi”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 63, no. 2, Rossiiskii universitet druzhby narodov, M., 2017, 278–315
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