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June 2008 Introduction to Boundary Value Problems of Nonlinear Elastostatics
Kazuaki Taira
Tsukuba J. Math. 32(1): 67-138 (June 2008). DOI: 10.21099/tkbjm/1496165193


This paper provides a careful and accessible exposition of an $L^p$ approach to boundary value problems of nonlinear elastostatics in the case where solutions of the linearized problem correspond faithfully to those of the nonlinear problem, that is, in the case where there is no bifurcation. We prove that if the linearized problem has unique solutions, then so does the nonlinear one, nearby. This is done by using the linear $L^p$ theory and the inverse mapping theorem. The main theorem can be applied to the Saint Venant-Kirchhoff elastic material and the Hencky-Nadai elastoplastic material in a unified theory. The approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of partial differential equations.


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Kazuaki Taira. "Introduction to Boundary Value Problems of Nonlinear Elastostatics." Tsukuba J. Math. 32 (1) 67 - 138, June 2008.


Published: June 2008
First available in Project Euclid: 30 May 2017

zbMATH: 1146.74008
MathSciNet: MR2433018
Digital Object Identifier: 10.21099/tkbjm/1496165193

Rights: Copyright © 2008 University of Tsukuba, Institute of Mathematics


Vol.32 • No. 1 • June 2008
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