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Uniqueness theorems in linear elasticity

Author: R J Knops; Lawrence Edward Payne
Publisher: Berlin, New York, Springer-Verlag, 1971.
Series: Springer tracts in natural philosophy, v. 19.
Edition/Format:   Print book : EnglishView all editions and formats
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Genre/Form: Eindeutigkeitstheoreme
Additional Physical Format: Online version:
Knops, R.J. (Robin John).
Uniqueness theorems in linear elasticity.
Berlin, New York, Springer-Verlag, 1971
(OCoLC)610154776
Document Type: Book
All Authors / Contributors: R J Knops; Lawrence Edward Payne
ISBN: 3540052534 9783540052531 0387052534 9780387052533
OCLC Number: 200945
Description: ix, 130 pages 24 cm.
Contents: 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 Kirchhoff's 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.
Series Title: Springer tracts in natural philosophy, v. 19.
Responsibility: [by] R.J. Knops [and] L.E. Payne.

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