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A New Variational Characterization of Sobolev Spaces

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Abstract

We obtain a new variational characterization of the Sobolev space \(W_p^1(\Omega )\) (where \(\Omega \subseteq \mathbb {R}^n\) and \(p>n\)). This is a generalization of a classical result of F. Riesz. We also consider some related results.

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Acknowledgments

The authors are grateful to the reviewer for his/her remarks.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Karlstad University, Universitetsgatan 2, 651-88 , Karlstad, Sweden

    Sorina Barza & Martin Lind

Authors
  1. Sorina Barza
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  2. Martin Lind
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Correspondence to Martin Lind.

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Communicated by Michael Lacey.

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Barza, S., Lind, M. A New Variational Characterization of Sobolev Spaces. J Geom Anal 25, 2185–2195 (2015). https://doi.org/10.1007/s12220-014-9508-z

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