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

  • Miroslav Bulíček
  • Jan Burczak


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.


Nonlinear small strain elasticity Regularity Fully nonlinear bulk modulus 

Mathematics Subject Classification

Primary 335J60 35Q74 35B65 Secondary 74G40 


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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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