Author | Knops, Robin John. author |
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Title | Uniqueness Theorems in Linear Elasticity [electronic resource] / by Robin John Knops, Lawrence Edward Payne |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1971 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65101-4 |
Descript | X, 132 p. online resource |
1 Introduction -- 2 Basic Equations -- 2.1 Formulation of Initial-Boundary Value Problems -- 2.2 The Classical and Weak Solutions -- 2.3 The Homogeneous Isotropic Body. Plane Elasticity -- 2.4 Definiteness Properties of the Elasticities -- 3 Early Work -- 4 Modern Uniqueness Theorems in Three-Dimensional Elastostatics -- 4.1 The Displacement Boundary Value Problem for Bounded Regions -- 4.2 Exterior Domains -- 4.3 The Traction Boundary Value Problem -- 4.4 Mixed Boundary Value Problems -- 5 Uniqueness Theorems in Homogeneous Isotropic Two-Dimensional Elastostatics -- 5.1 Kirchhoffโs Theorem in Two-Dimensions. The Displacement and Traction Boundary Value Problems -- 5.2 Uniqueness in Plane Problems with Special Geometries -- Appendix: Uniqueness of Three-Dimensional Axisymmetric Solutions -- 6 Problems in the Whole- and Half-Space -- 6.1 Specification of the Various Boundary Value Problems. Continuity onto the Boundary and in the Neighbourhood of Infinity -- 6.2 Uniqueness of Problems (a)-(d). Corollaries for the Space EN -- 6.3 Uniqueness for the Mixed-Mixed Problem of Type (e) -- 7 Miscellaneous Boundary Value Problems -- 7.1 Problems for a Sphere -- 7.2 The Cauchy Problem for Isotropic Elastostatics -- 7.3 The Signorini Problem. Other Problems with Ambiguous Conditions -- 8 Uniqueness Theorems in Elastodynamics. Relations with Existence, Stability, and Boundedness of Solutions -- 8.1 The Initial Displacement and Mixed-Boundary Value Problems. Energy Arguments -- 8.2 The Initial-Displacement Boundary Value Problem. Analyticity Arguments -- 8.3 The Initial-Mixed Boundary Value Problem for Bounded Regions. Further Arguments -- 8.4 Summary of Existing Results in the Uniqueness of Elastodynamic Solutions -- 8.5 Non-Standard Problems, including those with Ambiguous Conditions -- 8.6 Stability, Boundedness, Existence and Uniqueness -- References