Existence and smoothness for a class of $n$D models in elasticity theory of small deformations

Miroslav Bulíček; Jan Burczak

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arXiv · 1612.00803

Existence and smoothness for a class of $n$D models in elasticity theory of small deformations

Miroslav Bulíček·Jan Burczak

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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 regularity result for elasticity problems that covers the most natural space dimension $3$ and that captures behaviour of many typical elastic materials (considered in the small deformations) like rubber, polymer gels or concrete.

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BibTeX RIS

Miroslav Bulíček, Jan Burczak. 2016-12-02. Existence and smoothness for a class of $n$D models in elasticity theory of small deformations. https://arxiv.org/abs/1612.00803

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