We consider degenerate elliptic systems like the p-Laplacian system with p>1 and zero boundary data. The r.h.s. is given in divergence from div F. We prove a pointwise estimate (in terms of the sharp maximal function) bounding the gradient of the solution via the function F. This recovers several known results about local regularity estimates in L^q, BMO and C^a. Our pointwise inequality extends also to boundary points. So these regularity estimates hold globally as well. The global estimates in BMO and C^a are new.
- OxPDE Special Seminar