Literature cited
M. Schechter, “A generalization of the problem of transmission,” Ann. Sc. Norm. Super. Pisa,14, Fasc. III, 207–236 (1960).
Ya. A. Roitberg and Z. G. Sheftel', “General boundary-value problems for elliptic equations with discontinuous coefficients,” Dokl. Akad. Nauk SSSR,148, No. 5 (1963).
Ya. A. Roitberg, “Inhomogeneous elliptic problems with discontinuous coefficients, and local improvement of the smoothness of the generalized solutions up to the boundary of the domain and surface of discontinuity of the coefficients,” Third All-Union Symposium on Wave Diffraction (Abstracts of Papers) [in Russian], Nauka, Moscow (1964).
Ya. A. Roitberg, “A theorem on homeomorphisms realized in Lp by elliptic operators, and local improvement of the smoothness of the generalized solutions,” Ukrainsk. Matem. Zh.,17, No. 5 (1965).
Z. G. Sheftel', “Energy inequalities and general boundary-value problems for elliptic equations with discontinuous coefficients,” Sibirsk. Matem. Zh.,6, No. 3 (1965).
Ya. A. Roitberg, “Theory of the solvability in distributions of general boundary-value problems for elliptic equations,” Author's Abstract of Candidate's Dissertation, Chernigov Pedagogical Institute (1968).
Ya. A. Roitberg, “Theorems on homeomorphisms and a Green's formula for general elliptic boundary-value problems with nonnormal boundary conditions,” Matem. Sb.,83(125), No. 2(10) (1970).
Yu. M. Berezanskii, Eigenfunction Expansion, of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
Ya. A. Roitberg, “On the values on the domain boundary of the generalized solutions of elliptic equations,” Matemn. Sb.,86(128), No. 2(10) (1971).
Yu. V. Kostarchuk and Ya. A. Roitberg, “Theorems on isomorphisms for elliptic boundary-value problems with nonnormal boundary conditions,” Ukrainsk. Matem. Zh.,25, No. 2 (1973).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 28, No. 2, pp. 194–202, March–April, 1976.
In conclusion, the author sincerely thanks Ya. A. Roitberg and Yu. M. Berezanskii for suggesting the problem and discussing the results.
Rights and permissions
About this article
Cite this article
Kostarchuk, Y.V. A Green's formula and theorems on isomorphisms for general elliptic boundary-value problems with discontinuous coefficients, without assuming normal boundary conditions and conjugation conditions. Ukr Math J 28, 147–153 (1976). https://doi.org/10.1007/BF01085904
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01085904