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.
Second order regularity for degenerate p-Laplace type equations with log-concave weights
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We consider weighted p-Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log-concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp global second-order estimates. For unbounded domains, we prove local estimates at the boundary. The results are new even for the case p = 2.
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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.