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Boundary Value Problems of Finite Elasticity - Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data (Paperback, Softcover reprint of the original 1st ed. 1988)
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Boundary Value Problems of Finite Elasticity - Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data (Paperback, Softcover reprint of the original 1st ed. 1988)
Series: Springer Tracts in Natural Philosophy, 31
Expected to ship within 10 - 15 working days
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In this book I present, in a systematic form, some local theorems
on existence, uniqueness, and analytic dependence on the load,
which I have recently obtained for some types of boundary value
problems of finite elasticity. Actually, these results concern an
n-dimensional (n ~ 1) formal generalization of three-dimensional
elasticity. Such a generalization, be sides being quite
spontaneous, allows us to consider a great many inter esting
mathematical situations, and sometimes allows us to clarify certain
aspects of the three-dimensional case. Part of the matter presented
is unpublished; other arguments have been only partially published
and in lesser generality. Note that I concentrate on simultaneous
local existence and uniqueness; thus, I do not deal with the more
general theory of exis tence. Moreover, I restrict my discussion to
compressible elastic bodies and I do not treat unilateral problems.
The clever use of the inverse function theorem in finite elasticity
made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local
existence and uniqueness for the traction problem in
hyperelasticity under dead loads, inspired many of the ideas which
led to this monograph. Chapter I aims to give a very brief
introduction to some general concepts in the mathematical theory of
elasticity, in order to show how the boundary value problems
studied in the sequel arise. Chapter II is very technical; it
supplies the framework for all sub sequent developments.
General
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