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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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