Short note on global spatial regularity in elasto-plasticity with linear hardening
Please always quote using this URN:urn:nbn:de:0296-matheon-5183
- We study the global spatial regularity of solutions of elasto-plastic models with linear hardening. In order to point out the main idea, we consider a model problem on a cube, where we describe Dirichlet and Neumann boundary conditions on the top and the bottom, respectively, and periodic boundary conditions on the remaining faces. Under natural smoothness assumptions on the data we obtain $u\in L^\infty((0,T);H^{3/2-\delta}(\Omega))$ for the displacements and $z\in L^\infty((0,T);H^{1/2-\delta}(\Omega))$ for the internal variables. The proof is based on a difference quotient technique and a reflection argument.
Author: | Dorothee Knees |
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URN: | urn:nbn:de:0296-matheon-5183 |
Referee: | Carsten Carstensen |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2008/02/07 |
Release Date: | 2008/01/07 |
Tag: | |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions |
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Nxx Miscellaneous topics / 49N60 Regularity of solutions | |
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials) | |
Preprint Number: | 513 |