Higher integrability of the gradient in linear elasticity (Q1337515)

The authors investigate higher integrability of the gradient of the solution to a displacement-traction problem that is defined on a bounded \(C^ 1\) domain of \(R^ n\) associated with the linear elasticity equations with \(L^ \infty\) coefficients. This result is established by use of the technique of reverse Hölder inequalities, in which certain interior and boundary estimates are obtained for a local Hardy-Littlewood maximal operator of the gradient. An appropriate interplay between the Sobolev-Poincaré inequality, the Korn inequality and the local geometry of the domain near the interface of the two different boundary conditions plays a major role in establishing these estimates.