ISBN: 3540413979
TITEL: Lecture Notes in Mathematics, Vol. 1749
AUTHOR: 
TOC:

Introduction 1
1 Weak solutions to boundary value problems in the deformation theory of perfect elastoplasticity 5
1.0 Preliminaries 5
1.1 The classical boundary value problem for the equilibrium state of a perfect elastoplastic body and its primary functional formulation 6
1.2 Relaxation of convex variational problems in non reflexive spaces.
General construction 15
1.3 Weak solutions to variational problems of perfect elastoplasticity 27
2 Differentiability properties of weak solutions to boundary value problems in the deformation theory of plasticity 40
2.0 Preliminaries 40
2.1 Formulation of the main results 42
2.2 Approximation and proof of Lemma 2.1.1 52
2.3 Proof of Theorem 2.1.1 and a local estimate of Caccioppoli-type for the stress tensor 57
2.4 Estimates for solutions of certain systems of PDE's with constant coefficients 71
2.5 The main lemma and its iteration 76
2.6 Proof of Theorem 2.1.2 89
2.7 Open Problems 98
2.8 Remarks on the regularity of minimizers of variational Eunctionals from the deformation theory of plasticity with power hardening 100
Appendix A 107
A.1 Density of smooth functions in spaces of tensor-valued functions 107
A.2 Density of smooth functions in spaces of vector-valued functions 107
A.3 Some properties of the space BD (Ohm, R^n)
A.4 Jensen's inequality 126
3 Quasi-static fluids of generalized Newtonian type 131
3.0 Preliminaries 131
3.1 Partial C^1 regularity in variationale setting 143
3.2 Local boundedness of the strain velocity 167
3.3 The two-dimensional case 180
3.4 The Bingham variational inequality in dimensions two and three 193
3.5 Some open problems and comments concerning extensions 204
4 Fluids of Prandtl-Eyring type and plastic materials with loga-rithmic hardening law 207
4.0 Preliminaries 207
4.1 Some function spaces related to the Prandtl-Eyring fluid model 211
4.2 Existence of higher order weak derivatives and a Caccioppoli-type inequality 216
4.3 Blow-up: theproofofTheorem4.1.1forn=3 228
4.4 The two-dimensional case 235
4.5 Partial regularity for plastic materials with logarithmic hardening 237
4.6 A general class of constitutive relations 248
Appendix B 251
B.1 Density results 251
Notation and tools from functional analysis 254
Bibliography 260
Index 268
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