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# On the Local Hölder Continuity of the Inverse of the p-Laplace Operator

An Lê
Proceedings of the American Mathematical Society
Vol. 135, No. 11 (Nov., 2007), pp. 3553-3560
Stable URL: http://www.jstor.org/stable/20534985
Page Count: 8
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## Abstract

We prove an interpolation type inequality between $C^{\alpha}$ , $L^{\infty}$ and $L^{p}$ spaces and use it to establish the local Hölder continuity of the inverse of the p-Laplace operator: $\|(-\Delta _{p})^{-1}(f)-(-\Delta _{p})^{-1}(g)\|_{C^{1}(\overline{\Omega})}\leq C\|f-g\|_{L^{\infty}(\Omega)}^{r}$ , for any f and g in a bounded set in $L^{\infty}(\Omega)$ .

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