Existence and smoothness for a class of d-dimensional models in elasticity theory of small deformations
2018
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.