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Balci, Lars Diening, Markus Weimar","submitted_at":"2019-04-06T08:39:38Z","abstract_excerpt":"The paper is concerned with higher order Calderon-Zygmund estimates for the $p$-Laplace equation $$\n  -\\textrm{div}(A(\\nabla u))\n  := -\\textrm{div}{(|\\nabla\n  u|^{p-2}\\nabla u)}=-\\textrm{div} F, \\qquad 1<p<\\infty. $$ We are able to transfer local interior Besov and Triebel-Lizorkin regularity up to first order derivatives from the force term $F$ to the flux $A(\\nabla u)$. For $p\\geq 2$ we show that $F \\in B^s_{\\rho,q}$ implies $A(\\nabla u) \\in B^s_{\\rho,q}$ for any $s \\in (0,1)$ and all reasonable $\\rho,q \\in (0,\\infty]$ in the planar case. The result fails for $p<2$. 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Balci, Lars Diening, Markus Weimar","submitted_at":"2019-04-06T08:39:38Z","abstract_excerpt":"The paper is concerned with higher order Calderon-Zygmund estimates for the $p$-Laplace equation $$\n  -\\textrm{div}(A(\\nabla u))\n  := -\\textrm{div}{(|\\nabla\n  u|^{p-2}\\nabla u)}=-\\textrm{div} F, \\qquad 1<p<\\infty. $$ We are able to transfer local interior Besov and Triebel-Lizorkin regularity up to first order derivatives from the force term $F$ to the flux $A(\\nabla u)$. For $p\\geq 2$ we show that $F \\in B^s_{\\rho,q}$ implies $A(\\nabla u) \\in B^s_{\\rho,q}$ for any $s \\in (0,1)$ and all reasonable $\\rho,q \\in (0,\\infty]$ in the planar case. The result fails for $p<2$. 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