Abstract
For the weak solutions of second-order equations in a plane bounded domain, one obtains the asymptotics and estimates of the solutions near the interior angular points of the line of discontinuity of the coefficients. It is established that the number of terms of the asymptotics, not in the Sobolev classW 22 , can be arbitrarily large.
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Literature cited
E. M. Il'in, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., Akad. Nauk SSSR,38, 33–45 (1973).
R. B. Kellogg, Numerical Solutions of PDE, Vol. II, Academic Press, New York (1971), pp. 351–400.
V. A. Kondrat'ev, Tr. Mosk. Mat. 0-va.,16, 209–292 (1967).
Ya. A. Sovin, Dokl. Akad. Nauk SSSR,187, No. 5, 995–997 (1969).
Ya. A. Sovin, Author's Abstract of Dissertation, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1970).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR, Vol. 47, pp. 166–169, 1974.
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Il'in, E.M. Singularities of weak solutions of elliptic equations with discontinuous leading coefficients.. J Math Sci 9, 271–274 (1978). https://doi.org/10.1007/BF01578551
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DOI: https://doi.org/10.1007/BF01578551