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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).
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).
Yu. M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
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).
S. P. Gavelya, “ Solutions of linear elliptic systems of differential equations with discontinuous free terms,” Ukrainsk. Matem. Zh.,12 No.3 (1960).
I. M. Gel'fand and G.E. Shilov, Generalized Functions and Operators on Generalized Functions [in Russian], Moscow (1959).
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
- Elliptic Equation
- Power Singularity