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We begin by establishing a sharp (optimal) Wloc2,2-regularity result for bounded weak solutions to a nonlinear elliptic equation with the p-Laplacian, Δpu=defdiv(|∇u|p−2∇u), 1<p<∞. We develop very precise, optimal regularity estimates on the ellipticity of this degenerate (for 2<p<∞) or singular (for 1<p<2) problem. We apply this regularity result to prove Pohozhaevʼs identity for...