On the regularity up to the boundary for second order nonlinear elliptic systems
Mariano Giaquinta, Jindřich Nečas, Oldřich John, Jana Stará · Pacific Journal of Mathematics · 1982
In several earlier papers, the first two authors have shown that the question of interior regularity for solutions of boundary value problems for second-order nonlinear elliptic systems is equivalent (in some sense) to a certain Liouville property. The present paper demonstrates that a similar result is true for regularity up to the boundary of the uniformly Lipschitz-continuous weak solutions of the boundary value problems.