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Estimates for solutions of homogeneous elliptic linear equations defined on bounded domains

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Literature cited

  1. A. S. Fokht, “Inequalities for solutions of elliptic equations and their derivatives near the boundary of a domain in the L2 metric,” Proceedings of the Mathematics Institute of the Academy of Sciences of the USSR [in Russian], Vol. 77 (1965).

  2. A. S. Fokht, “Imbedding theorems for solutions of elliptic equations,” Proceedings of the Mathematics Institute of the Academy of Sciences of the USSR [in Russian], Vol. 105 (1969).

  3. A. S. Fokht, “Integral estimates for generalized derivatives of solutions of elliptic second-order equations in the Lp metric with p > 2, and related imbedding theorems,” Proceedings of the Mathematics Institute of the Academy of Sciences of the USSR [in Russian], Vol. 117 (1972).

  4. A. S. Fokht, “Estimates for generalized derivatives of solutions of second-order elliptic equations in the Lp metric with 1 < p < 2, and related imbedding theorems,” Differentsial'. Uravneniya (in press).

  5. A. S. Fokht, “Integral estimates for derivatives of solutions of homogeneous elliptic equations with reduced requirements on the smoothness class of the boundary of the domain,” Ukr. Matem. Zh.,24, No. 6 (1972).

  6. O. B. Besov, “Behavior of differentiable functions on nonsmooth surfaces,” Proceedings of the Mathematics Institute of the Academy of Sciences of the USSR [in Russian], Vol. 117 (1972).

  7. L. Schwartz, Theorie des Distributions, Vol. I, Hermann, Paris, 1950; Vol. II, 1951 (1957–1959).

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  8. H. Bremerman, Distributions, Complex Variables, and the Fourier Transforms, Addison-Wesley, Reading, Mass. (1965).

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  9. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Ed. 4, Nauka, Moscow (1968).

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Authors and Affiliations

  1. Moscow Institute of Physics and Engineering, USSR

    A. S. Fokht

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  1. A. S. Fokht
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 26, No. 6, pp. 845–849, November–December, 1974.

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Fokht, A.S. Estimates for solutions of homogeneous elliptic linear equations defined on bounded domains. Ukr Math J 26, 698–701 (1974). https://doi.org/10.1007/BF01085270

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  • DOI: https://doi.org/10.1007/BF01085270

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