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Isomorphism theorems and their applications for elliptic boundary-value problems with discontinuous coefficients, and boundary conditions and conjugacy conditions which are not normal

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Literature cited

  1. Yu. M. Berezanskii, Expansion of Self-Conjugate Operators by Means of Eigenfunctions [in Russian], Nauka, Dumka, Kiev (1965).

    Google Scholar 

  2. E. Madzhenes, “Interpolation spaces and partial differential equations,” Ukrainsk. Matem. Zh.,21, No. 2, 169–218 (1966).

    Google Scholar 

  3. S. G. Krein, “Interpolation of linear operators and the properties of solutions of elliptic equations,” in: Elliptische Differentialgleichungen [in Russian], Vol. II, Colloquium, Aug. 17–24, 1969 in-Berlin, Akademie-Verlag, Berlin (1971).

    Google Scholar 

  4. Ya. A. Roitberg, “Theorems on homeomorphisms and Green's formula for general elliptic boundary-value problems with boundary conditions which are not normal,” Matem. Sbor.,83, No. 2, 181–213 (1970).

    Google Scholar 

  5. Zh. -L. Lions and E. Madzhenes, Nonhomogeneous Boundary-Value Problems and Their Applications [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  6. Yu. V. Kostarchuk, “Green's formula and theorems on isomorphisms for general elliptic boundary — value problems with discontinuous coefficients without assuming normality of boundary conditions and conjugate conditions,” Ukrainsk. Matem. Zh.,28, No. 2, 194–202 (1976).

    Google Scholar 

  7. Ya. A. Roitberg, “A theorem on homeomorphisms established by elliptic operators,” Dokl. Akad. Nauk SSSR,180, No. 3, 542–545 (1968).

    Google Scholar 

  8. Yu. V. Kostarchuk and Ya. A. Roitberg, “Theorems on isomorphisms for elliptic boundary-value problems with boundary conditions which are not normal,” Ukrainsk. Matem. Zh.,25, No. 2, 277–283 (1973).

    Google Scholar 

  9. Ya. A. Roitberg, “Values on the boundary of the domain of generalized solutions of elliptic equations,” Matem. Sbor.,86(128), No. 2(10), 248–267 (1971).

    Google Scholar 

  10. Yu. M. Berezanskii and Ya. A. Roitberg, “Homeomorphism theorems and the Green function for general elliptic boundary-value problems,” Ukrainsk. Matem. Zh.,19, No. 5, 3–9 (1965).

    Google Scholar 

  11. Yu. V. Kostarchuk, “Local increase in smoothness in generalized solutions of elliptic boundary-value problems with boundary conditions which are not normal,” Ukrainsk. Matem. Zh.,25, No. 4, 536–541 (1973).

    Google Scholar 

  12. Yu. V. Kostarchuk, “General elliptic boundary-value problems with power singularities in their right-hand parts,” Ukrainsk. Matem. Zh.,25, No. 6, 798–804 (1973).

    Google Scholar 

  13. Yu. V. Kostarchuk, “General elliptic boundary-value problems with power singularities in their right-hand parts,” in: Approximation Methods for Integrating Differential and Integral Equations [in Russian], Kievskii Fed. Inst., Kiev (1973), pp. 76–87.

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 28, No. 4, pp. 532–537, July–August, 1976.

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Kostarchuk, Y.V. Isomorphism theorems and their applications for elliptic boundary-value problems with discontinuous coefficients, and boundary conditions and conjugacy conditions which are not normal. Ukr Math J 28, 412–416 (1976). https://doi.org/10.1007/BF01101663

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  • DOI: https://doi.org/10.1007/BF01101663

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