Partial regularity of weak solutions of quasilinear elliptic systems and weak Harnack inequalities.

Abstract

In this thesis we study quasilinear elliptic systems of p-Laplacian type with a perturbation satisfying a natural (critical) growth condition. First, using test functions recently introduced by R. Landes we deduce Caccioppoli-type inequality for bounded weak solutions of such systems. Then we modify the classical approach of Giaquinta and Giusti to obtain higher integrability and as a consequence partial Holder continuity of the above solution. Finally, we deduce weak Harnack inequalities for subsolutions and supersolutions for certain systems.