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Solvability of general boundary-value problems for elliptic equations with right-hand sides having power singularities

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Literature cited

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    Ya. A. Roitberg, “A theorem concerning homomorphisms in Lp realized by elliptic operators, and local increases in the smoothness of generalized solutions,” Ukrainsk. Matem.Zh., 17, No. 5 (1965).

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    Ya. A. Roitberg, “Elliptic boundary-value problems with inhomogeneous boundary conditions, and the local increase in the smoothness of generalized solutions up to the boundary,” Dokl. Akad. Nauk SSSR,157, No. 4, 798–801(1964).

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    Yu. M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

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    Yu. M. Berezanskii, S. G. Krein, and Ya. A. Roitberg, “A theorem concerning homomorphisms, and the local increase of smoothness of solutions of elliptic equations up to the boundary,” Dokl. Akad. Nauk SSSR,148, No.4, 745–748(1963).

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    S. P. Gavelya, “ Solutions of linear elliptic systems of differential equations with discontinuous free terms,” Ukrainsk. Matem. Zh.,12 No.3 (1960).

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    I. M. Gel'fand and G.E. Shilov, Generalized Functions and Operators on Generalized Functions [in Russian], Moscow (1959).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.20, No.3, pp.412–418, May–June, 1968.

The author wishes to thank Yu. M. Berezanskii for his interest in our work and for his valuable advice.

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Roitberg, Y.A. Solvability of general boundary-value problems for elliptic equations with right-hand sides having power singularities. Ukr Math J 20, 358–362 (1968). https://doi.org/10.1007/BF01085955

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Keywords

  • Elliptic Equation
  • Power Singularity