Author | Valent, Tullio. author |
---|---|
Title | Boundary Value Problems of Finite Elasticity [electronic resource] : Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data / by Tullio Valent |
Imprint | New York, NY : Springer New York, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3736-5 |
Descript | XII, 191 p. online resource |
I. A Brief Introduction to Some General Concepts in Elasticity -- ยง1. Some Notations -- ยง2. Deformations and Motions -- ยง3. Mass. Force -- ยง4. Eulerโs Axiom. Cauchyโs Theorem -- ยง5. Constitutive Assumptions. Elastic Body -- ยง6. Frame-Indifference of the Material Response -- II. Composition Operators in Sobolev and Schauder Spaces. Theorems on Continuity, Differentiability, and Analyticity -- ยง1. Some Facts About Sobolev and Schauder Spaces -- ยง2. A Property of Multiplication in Sobolev Spaces -- ยง3. On Continuity of Composition Operators in Sobolev and Schauder Spaces -- ยง4. On Differentiability of Composition Operators in Sobolev and Schauder Spaces -- ยง5. On Analyticity of Composition Operators in Sobolev and Schauder Spaces -- ยง6. A Theorem on Failure of Differentiability for Composition Operators -- III. Dirichlet and Neumann Boundary Problems in Linearized Elastostatics. Existence, Uniqueness, and Regularity -- ยง1. Kornโs Inequalities -- ยง2. A Generalization of a Theorem of Lax and Milgram -- ยง3. Linearized Elastostatics -- ยง4. The Dirichlet Problem in Linearized Elastostatics. Existence and Uniqueness in W1,p(?, ?n) -- ยง5. The Neumann Problem in Linearized Elastostatics. Existence and Uniqueness in W1,p(?, ? n) -- ยง6. Some Basic Inequalities for Elliptic Operators -- ยง7. Regularity Theorems for Dirichlet and Neumann Problems in Linearized Elastostatics -- IV. Boundary Problems of Place in Finite Elastostatics -- ยง1. Formulation of the Problem -- ยง2. Remarks on Admissibility of a Linearization -- ยง3. A Topological Property of Sets of Admissible Deformations -- ยง4. Local Theorems on Existence, Uniqueness, and Analytic Dependence on f for Problem ((1.1), (1.3)) -- ยง5. Stronger Results on Existence and Uniqueness for Problem ((1.1), (1.3)) -- ยง6. Local Theorems on Existence and Uniqueness for Problem ((1.1), (1.2)) -- V. Boundary Problems of Traction in Finite Elastostatics. An Abstract Method. The Special Case of Dead Loads -- ยง1. Generality on the Traction Problem in Finite Elastostatics -- ยง2. Preliminary Discussion -- ยง3. A Basic Lemma -- ยง4. Critical Infinitesimal Rigid Displacements for a Load -- ยง5. A Local Theorem on Existence, Uniqueness, and Analytic Dependence on a Parameter -- ยง6. The Case of Dead Loads -- ยง7. Some Historical Notes -- VI. Boundary Problems of Pressure Type in Finite Elastostatics -- ยง1. Preliminaries -- ยง2. The Case When the Load Is Invariant Under Translations -- ยง3. The Case When the Load Is Invariant Under Rotations -- ยง4. The Case of a Heavy Elastic Body Submerged in a Quiet Heavy Liquid -- Appendix I. On Analytic Mappings Between Banach Spaces. Analytic Implicit Function Theorem -- Appendix II. On the Representation of Orthogonal Matrices -- Index of Notations