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Mixed Boundary Value Problems for the Elasticity System in Exterior Domains

1
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilov str., 40, Moscow 119333, Russia
2
Steklov Mathematical Institute, Russian Academy of Sciences, Gubkin str., 8, Moscow 119991, Russia
3
Moscow Aviation Institute (National Research University), Volokolomskoe shosse, 4, Moscow 125993, Russia
Math. Comput. Appl. 2019, 24(2), 58; https://doi.org/10.3390/mca24020058
Received: 26 March 2019 / Revised: 24 May 2019 / Accepted: 31 May 2019 / Published: 2 June 2019
(This article belongs to the Special Issue Related Problems of Continuum Mechanics)
We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight | x | a is finite for such solutions. We use the variational principle and depending on the value of the parameter a, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions. View Full-Text
Keywords: elasticity system; Dirichlet–Robin problem; Neumann–Robin problem; Sobolev space; weighted energy integral elasticity system; Dirichlet–Robin problem; Neumann–Robin problem; Sobolev space; weighted energy integral
MDPI and ACS Style

Matevossian, H.A. Mixed Boundary Value Problems for the Elasticity System in Exterior Domains. Math. Comput. Appl. 2019, 24, 58.

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