Open Access
2019 Characterization of Sobolev-Slobodeckij Spaces Using Curvature Energies
Damian Dąbrowski
Publ. Mat. 63(2): 663-677 (2019). DOI: 10.5565/PUBLMAT6321907


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. "Characterization of Sobolev-Slobodeckij Spaces Using Curvature Energies." Publ. Mat. 63 (2) 663 - 677, 2019.


Received: 2 November 2017; Revised: 9 May 2018; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07094865
MathSciNet: MR3980936
Digital Object Identifier: 10.5565/PUBLMAT6321907

Primary: 46E35 , 53A07

Keywords: geometric curvature energies , Menger curvature , Sobolev-Slobodeckij spaces

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 2 • 2019
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