I. A Brief Introduction to Some General Concepts in Elasticity. - 1. Some Notations. - 2. Deformations and Motions. - 3. Mass. Force. - 4. Euler's Axiom. Cauchy's Theorem. - 5. Constitutive Assumptions. Elastic Body. - 6. Frame-Indifference of the Material Response. - II. Composition Operators in Sobolev and Schauder Spaces. Theorems on Continuity Differentiability and Analyticity. - 1. Some Facts About Sobolev and Schauder Spaces. - 2. A Property of Multiplication in Sobolev Spaces. - 3. On Continuity of Composition Operators in Sobolev and Schauder Spaces. - 4. On Differentiability of Composition Operators in Sobolev and Schauder Spaces. - 5. On Analyticity of Composition Operators in Sobolev and Schauder Spaces. - 6. A Theorem on Failure of Differentiability for Composition Operators. - III. Dirichlet and Neumann Boundary Problems in Linearized Elastostatics. Existence Uniqueness and Regularity. - 1. Korn's Inequalities. - 2. A Generalization of a Theorem of Lax and Milgram. - 3. Linearized Elastostatics. - 4. The Dirichlet Problem in Linearized Elastostatics. Existence and Uniqueness in W1p(? ?n). - 5. The Neumann Problem in Linearized Elastostatics. Existence and Uniqueness in W1p(? ? n). - 6. Some Basic Inequalities for Elliptic Operators. - 7. Regularity Theorems for Dirichlet and Neumann Problems in Linearized Elastostatics. - IV. Boundary Problems of Place in Finite Elastostatics. - 1. Formulation of the Problem. - 2. Remarks on Admissibility of a Linearization. - 3. A Topological Property of Sets of Admissible Deformations. - 4. Local Theorems on Existence Uniqueness and Analytic Dependence on f for Problem ((1. 1) (1. 3)). - 5. Stronger Results on Existence and Uniqueness for Problem ((1. 1) (1. 3)). - 6. LocalTheorems 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. - 1. Generality on the Traction Problem in Finite Elastostatics. - 2. Preliminary Discussion. - 3. A Basic Lemma. - 4. Critical Infinitesimal Rigid Displacements for a Load. - 5. A Local Theorem on Existence Uniqueness and Analytic Dependence on a Parameter. - 6. The Case of Dead Loads. - 7. Some Historical Notes. - VI. Boundary Problems of Pressure Type in Finite Elastostatics. - 1. Preliminaries. - 2. The Case When the Load Is Invariant Under Translations. - 3. The Case When the Load Is Invariant Under Rotations. - 4. 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. Language: English