Applying the universal iterative process to some problems of mechanics

The iterative universal process, which was introduced by the author some years ago, is applied to quasilinear boundary value problems in elasticity and filtration. It is proved that the method converges both in weak (energy) and strong (C ^γ(γ > 0)). Some results concerning the existence of weak and regular solutions are proved. The proof is based on general results such as the Korn inequality for weighted spaces and the method of elastic solutions.The main results also contain the Hölder continuity of displacements for elasto-plastic media with hardening.