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On regularity of generalized solutions of the third boundary-value problem for an elliptic difference-differential equation

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Abstract

Unlike the case of elliptic differential equations, generalized solutions of elliptic difference-differential equations may be not smooth in a domainQ but remain smooth only in certain subdomainsQ r ⊂Q Conditions are considered which are necessary and sufficient for generalized solutions of the third boundary-value problem to preserve smoothness on the boundary of adjacent subdomainsQ r .

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Authors and Affiliations

  1. Moscow Aircraft Institute, USSR

    E. L. Tsvetkov

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  1. E. L. Tsvetkov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.47, No. 1, pp. 93–104, January, 1995.

The author expresses his deep gratitude to A. D. Myshkis and A. L. Skubachevskii for helpful discussions.

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Tsvetkov, E.L. On regularity of generalized solutions of the third boundary-value problem for an elliptic difference-differential equation. Ukr Math J 47, 107–120 (1995). https://doi.org/10.1007/BF01058800

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  • DOI: https://doi.org/10.1007/BF01058800

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