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arXiv · 1710.00263

Characterization of Sobolev-Slobodeckij spaces using curvature energies

Damian Dąbrowski
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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.

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Damian Dąbrowski. 2017-09-30. Characterization of Sobolev-Slobodeckij spaces using curvature energies. https://doi.org/10.5565/publmat6321907

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