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Estimates for solutions of the Dirichlet problem for the biharmonic equation in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity. Saint-Venant's principle

Published online by Cambridge University Press:  14 November 2011

Y. A. Kondratiev  and
O. A. Oleinik
Y. A. Kondratiev
Affiliation:
Moscow University, U.S.S.R
O. A. Oleinik
Affiliation:
Moscow University, U.S.S.R
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Synopsis

In this paper energy estimates for solutions of the Dirichlet problem for the biharmonicequation, expressing Saint-Venant's principle in elasticity, are proved. From these integral inequalities, estimates for the maximum modulus of solutions and the gradient of solutions with homogeneous Diriehlet's boundary conditions in a neighbourhood of an irregular boundary point or in a neighbourhood of infinity are derived. These estimates characterize the continuity of solutions and their gradients at these points.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 3-4 , 1983 , pp. 327 - 343
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

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