Some estimates for the oscillation of the deformation gradient

As a measure of deformation we can take the difference D - R, where D is the deformation gradient of the mapping and R is the deformation gradient of the mapping , which represents some proper rigid motion. In this article, the norm is estimated by means of the scalar measure e() of nonlinear strain. First, the estimates are given for a deformation W^1,p() satisfying the condition . Then we deduce the estimate in the case that (x) is a bi-Lipschitzian deformation and .