# Characterization of Sobolev-Slobodeckij spaces using geometric curvature energies

@article{Dbrowski2019CharacterizationOS, title={Characterization of Sobolev-Slobodeckij spaces using geometric curvature energies}, author={Damian Dąbrowski}, journal={Publicacions Matem{\`a}tiques}, year={2019} }

The aim of this paper is to give a new characterization of Sobolev-Slobodeckij spaces W^{1+s,p} for p > n and n/p < s < 1, where n is the dimension of the domain. To achieve this we introduce a family of geometric curvature energies - functionals on the space of surfaces 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 Lipschitz continuous and its graph has finite geometric curvature energy of…

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