Published Paper

Inserted: 20 feb 2017
Last Updated: 20 feb 2017

Journal: J. Differential Equations
Year: 2016

Abstract:

We strengthen the classical inequality of C. B. Morrey concerning the optimal Hölder continuity of functions in $W^{1,p}$ when $p>n$, by replacing the $L^p$-modulus of the gradient with the sharp Hardy difference involving distance to the boundary. When $p=n$ we do the same strengthening in the integral form of a well known inequality due to F. John and L. Nirenberg.

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• HardyMorrey_JDE.pdf