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Title: Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I (English)
Author: Rektorys, Karel
Author: Danešová, Jana
Author: Matyska, Jiří
Author: Vitner, Čestmír
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 22
Issue: 5
Year: 1977
Pages: 349-394
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Category: math
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Summary: For a simly connected region, the solution of the first problem of plane elasticity can be reduced - roughly speaking - to the solution of a biharmonic problem. This problem can then be solved approximately by the method of least squares on the boundary, developed by K. Rektorys and V. Zahradník in Apl. mat. 19 (1974), 101-131. The present paper gives a generalization of this method for multiply connected regions. Two fundamental questions which arise in this case are answered, namely: (i) How to formulate the problem in order that it correspond to the reality. (ii) How to modify the method and prove the convergence. ()
MSC: 31B30
MSC: 35J40
MSC: 65M12
MSC: 74B20
MSC: 74B99
MSC: 74H99
idZBL: Zbl 0384.31005
idMR: MR0446010
DOI: 10.21136/AM.1977.103712
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Date available: 2008-05-20T18:08:03Z
Last updated: 2020-07-28
Stable URL: http://hdl.handle.net/10338.dmlcz/103712
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Reference: [1] K. Rektorys V. Zahradník: Solution of the First Biharmonic Problem by the Method of Least Squares on the Boundary.Apl. mat. 19 (1974), No. 2, 101 - 131. MR 0346312
Reference: [2] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Praha, Akademia 1967. MR 0227584
Reference: [3] K. Rektorys: Variational Methods.In Czech: Praha, SNTL 1974. In English: Dordrecht (Holland) - Boston (U.S.A.) Reidel Co 1977. Zbl 0371.35001, MR 0487653
Reference: [4] I. Babuška K. Rektorys F. Vyčichlo: Mathematische Elastizitätstheorie der ebenen Probleme.In Czech: Praha, NČSAV 1955. In German: Berlin, Akademieverlag 1960. MR 0115343
Reference: [5] I. Hlaváček J. Naumann: Inhomogeneous Boundary Value Problems for the von Kármán Equations.Apl. mat.: Part I 1974, No. 4, p. 253-269; Part II 1975, No. 4, p. 280-297.
Reference: [6] W. Rudin: Real and Complex Analysis.London-New York-Sydney-Toronto, McGraw-Hill 1970.
Reference: [7] S. G. Michlin: Variational Methods in Mathematical Physics.(In Russian.) 2. Ed., Moskva, Nauka 1970. MR 0353111
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