Solutions of the Robin Problem for the System of Elastic Theory in External Domains
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One considers the Robin problem for the linear system of elastic theory. Properties of its solutions are examined in the classes of functions with bounded energy integral with the power weight |x| a . For different values of the weight parameter a, uniqueness theorems are proved and exact formulas are obtained for the dimension of the space of solutions of the Robin problem in external domains.
KeywordsWeak Solution Triangle Inequality Elastic Theory Unbounded Domain Independent Solution
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- 1.G. Fichera, Existence Theorems in Elasticity [Russian translation], Mir, Moscow (1974).Google Scholar
- 4.V. A. Kondratiev and O. A. Oleinik, “On time-periodic solutions of a second-order parabolic equation in unbounded domains,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 4, 38–47 (1985).Google Scholar
- 7.Y. V. Mikhailova, “Mixed boundary-value problem for the system of elasticity in unbounded domains,” Tr. Semin. Petrovskogo, 18, 106–156 (1995).Google Scholar
- 8.A. A. Kon’kov, “On the dimension of the space of solutions of elliptic systems in unbounded domains,” Mat. Sb., 184, No. 12, 23–52 (1993).Google Scholar
- 9.L. D. Kudryavtsev, “Solution of the first boundary-value problem for self-adjoint and elliptic equations in unbounded domains,” Izv. Akad. Nauk SSSR, Ser. Mat., 31, No. 5, 354–366 (1967).Google Scholar
- 15.Ya. B. Lopatinskii, Theory of General Boundary-Value Problem: Selected Works [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
- 17.S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977).Google Scholar