Boundary Value Problems of Finite Elasticity

1. Front Matter

   Pages i-xii

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2. A Brief Introduction to Some General Concepts in Elasticity

   • Tullio Valent

   Pages 1-15

3. Composition Operators in Sobolev and Schauder Spaces. Theorems on Continuity, Differentiability, and Analyticity

   • Tullio Valent

   Pages 16-52

4. Dirichlet and Neumann Boundary Problems in Linearized Elastostatics. Existence, Uniqueness, and Regularity

   • Tullio Valent

   Pages 53-86

5. Boundary Problems of Place in Finite Elastostatics

   • Tullio Valent

   Pages 87-101

6. Boundary Problems of Traction in Finite Elastostatics. An Abstract Method. The Special Case of Dead Loads

   • Tullio Valent

   Pages 102-131

7. Boundary Problems of Pressure Type in Finite Elastostatics

   • Tullio Valent

   Pages 132-170

8. Back Matter

   Pages 171-193

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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 Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality.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.

• Implicit function
• banach spaces
• deformation
• development
• elasticity
• elastostatics
• material
• measure
• statics

• Dipartimento di Matematica Pura ed Applicata, Università di Padova, Padova, Italy

  Tullio Valent

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