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The vertex of a cone can be nonregular in the Wiener sense for a fourth-order elliptic equation

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Literature cited

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    V. G. Maz'ya, “Behavior of solutions to the Dirichlet problem for the biharmonic operator at a boundary point,” Lect. Notes Math.,703, 250–262 (1979).

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    V. G. Maz'ya and T. Donchev, “On the Wiener regularity of a boundary point for a polyharmonic operator,” Dokl. Bolg. Akad. Nauk,36, No. 2, 177–179 (1983).

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    V. G. Maz'ya and B. A. Plamenevskii, “On a maximum principle for the biharmonic equation in a domain with conical points,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 52–59 (1981).

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    V. G. Maz'ya, S. A. Nazarov, and B. A. Plamenevskii, “On homogeneous solutions of the Dirichlet problem in the exterior of a thin cone,” Dokl. Akad. Nauk SSSR,226, No. 2, 281–284 (1982).

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    V. G. Maz'ya, S. A. Nazarov, and B. A. Plamenevskii, “On singularities of solutions of the Dirichlet problem in the exterior of a thin cone,” Mat. Sb.,122, No. 4, 435–456 (1983).

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    I. M. Gel'fand and G. E. Shilov, Generalized Functions and Operations on Them, Academic Press (1968).

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    L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. 1, Springer-Verlag, Berlin (1983).

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    B.-W. Schulze and G. Wildenhain, Methoden der Potentialtheorie für elliptische Differentialgleichungen beliebigen Ordnung, Akademie-Verlag, Berlin (1977), p. 408.

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Translated from Matematicheskie Zametki, Vol. 39, No. 1, pp. 24–28, January, 1986.

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Maz'ya, V.G., Nazarov, S.A. The vertex of a cone can be nonregular in the Wiener sense for a fourth-order elliptic equation. Mathematical Notes of the Academy of Sciences of the USSR 39, 14–16 (1986). https://doi.org/10.1007/BF01647626

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Keywords

  • Elliptic Equation