Abstract
We construct and study self-adjoint operators corresponding to problems mentioned in the title. We describe a correlation between domains of definition of fractional powers of these operators and Sobolev spaces. We state new results on the solvability of several problems for nonlinear parabolic equations which have not yet been studied.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 374–381, March, 1991.
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Nizhnik, L.P., Taraborkin, L.A. On self-adjoint operators generated by nonhomogeneous elliptic problems with discontinuous boundary conditions and conjugation conditions. Ukr Math J 43, 338–345 (1991). https://doi.org/10.1007/BF01670074
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DOI: https://doi.org/10.1007/BF01670074