On the Regularity of Stresses in the Closed Domain for the Linear Theory of Elasticity

The article deals with the estimates of the first derivatives of the solutions of the system L(u) u + ( + )(u) = –f(x). The solutions are fixed at the boundary u| = 0. The estimates are obtained in the whole closed domain in terms of the right-hand term f in a certain strong norm. If the norm of f in l ₂ is sufficiently small as compared to its strong norm, one can obtain estimates in an explicit form.