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Existence and smoothness for a class of d-dimensional models in elasticity theory of small deformations

  • Miroslav Bulíček
  • Jan Burczak
Article

Abstract

We consider a model for deformations of a homogeneous isotropic body, whose shear modulus remains constant, but its bulk modulus can be a highly nonlinear function. We show that for a general class of such models, in an arbitrary space dimension, the respective PDE problem has a unique solution. Moreover, this solution enjoys interior smoothness. This is the first full regularity result for elasticity problems that covers the most natural space dimension 3 and that captures the behaviour of real-life elastic materials (considered in small deformations), primarily certain beta-phase titanium alloys.

Keywords

Nonlinear small strain elasticity Regularity Fully nonlinear bulk modulus 

Mathematics Subject Classification

Primary 335J60 35Q74 35B65 Secondary 74G40 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical InstituteCharles UniversityPrague 8Czech Republic
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland
  3. 3.OxPDE, Mathematical InstituteUniversity of OxfordOxfordUK

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