For quasilinear equations -div(a(|∇u|)∇u)=f, the stress field a(|∇u|)^k∇u is shown to belong to W^{1,2}(Ω) up to the boundary for the optimal range of k, under weak W^{2,X} boundary regularity, with a convex-domain version requiring no boundary regularity.
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Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
For quasilinear equations -div(a(|∇u|)∇u)=f, the stress field a(|∇u|)^k∇u is shown to belong to W^{1,2}(Ω) up to the boundary for the optimal range of k, under weak W^{2,X} boundary regularity, with a convex-domain version requiring no boundary regularity.