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Singularities of weak solutions of elliptic boundary-value problems with discontinuous leading coefficients

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Literature cited

  1. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).

    Google Scholar 

  2. M. Sh. Birman and G. E. Skvortsov, “On the square summability of the highest derivatives of the solution of the Dirichlet problem in a domain with a piecewise smooth boundary,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 5 (1962).

  3. G. M. Berzhbinskii, “On the deficiency index of the second and the third boundary-value problem in a domain with a piecewise smooth boundary,” Vestn. LGU, Ser. Mat, Mekh. Astr., No. 7, 1610–162 (1964).

    Google Scholar 

  4. G. M. Berzhbinskii, “The behavior of the solutions of certain elliptic boundary-value problems in domains with nonregular boundaries,” Dissertation, Leningr. Gos. Ped. Inst. (1968).

  5. V. A. Kondrat'ev, “Boundary-value problems for elliptic equations in domains with conical or angular points,” Tr. Mosk. Ob-va,16, 209–292 (1967).

    Google Scholar 

  6. L. A. Oganesyan and L. A. Rukhovets, “On variational-difference schemes for linear second order elliptic equations in a two-dimensional domain with a piecewise smooth boundary,” Zh. Vychisl. Mat. Mat. Fiz.,8, No. 1, 97–114 (1968).

    Google Scholar 

  7. L. A. Oganesyan, V. Ya. Rivkind, and B. A. Samokish, “Variational-difference schemes in the problems of electronic optics. Methods of calculation of electrono-optic systems,” Tr. Sh-go Vsesoyuznogo Seminara VTs SO Akad. Nauk SSSR, Novosibirsk (1970).

  8. L. N. Slobodetskii, “Generalized Sobolev spaces and their application to boundary-value problems for partial differential equations,” Uch. Zap. Leningr. Gos. Ped. Inst. (1958), p. 197.

  9. G. N. Yakovlev, “Boundary properties of functions of class W (ℓ)p in domains with angular points,” Dokl. Akad. Nauk SSSR,140, No. 1 (1961).

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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. Vol. 38, pp. 33–45, 1973.

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Il'in, E.M. Singularities of weak solutions of elliptic boundary-value problems with discontinuous leading coefficients. J Math Sci 8, 373–384 (1977). https://doi.org/10.1007/BF01084610

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