Abstract
We give a new characterization of Sobolev-Slobodeckij spaces $W^{1+s,p}$ for $n/p< 1+s$, where $n$ is the dimension of the domain. To achieve this we introduce a family of curvature energies inspired by the classical concept of integral Menger curvature. We prove that a function belongs to a Sobolev-Slobodeckij space if and only if it is in $L^p$ and the appropriate energy is finite.
Citation
Damian Dąbrowski. "Characterization of Sobolev-Slobodeckij Spaces Using Curvature Energies." Publ. Mat. 63 (2) 663 - 677, 2019. https://doi.org/10.5565/PUBLMAT6321907
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