Quasilinear elliptic equations on convex domains

We show global regularity for p  -Laplacian type elliptic equations on convex domains with W1,q(q≥p>1)W1,q(q≥p>1) boundary data. The maximal function, Vitali covering lemma and approximation (or compactness method) are the main techniques in the proof. To derive the approximation lemma, we need W1,∞W1,∞ estimates for the corresponding homogeneous equations, where the convexity of the domain plays an important role.