Article
MSC:
31B30,
35J40,
65M12,
74B20,
74B99,
74H99 | MR 0446010 | Zbl 0384.31005 | DOI: 10.21136/AM.1977.103712
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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.
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References:
[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
[2] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Praha, Akademia 1967. MR 0227584
[3] K. Rektorys: Variational Methods. In Czech: Praha, SNTL 1974. In English: Dordrecht (Holland) - Boston (U.S.A.) Reidel Co 1977. MR 0487653 | Zbl 0371.35001
[4] I. Babuška K. Rektorys F. Vyčichlo: Mathematische Elastizitätstheorie der ebenen Probleme. In Czech: Praha, NČSAV 1955. In German: Berlin, Akademieverlag 1960. MR 0115343
[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.
[6] W. Rudin: Real and Complex Analysis. London-New York-Sydney-Toronto, McGraw-Hill 1970.
[7] S. G. Michlin: Variational Methods in Mathematical Physics. (In Russian.) 2. Ed., Moskva, Nauka 1970. MR 0353111
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