On the local Hölder continuity of the inverse of the $p$-Laplace operator
On the local Hölder continuity of the inverse of the $p$-Laplace operator
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: $\|(-\Delta _p)^{-1}(f) - (-\Delta _p)^{-1}(g)\|_{C^{1}(\bar {\Omega })} \leq C \| f - g \|^r_{L^\infty (\Omega )}$, for any $f$ and $g$ in …