A new characterization of Sobolev spaces
By Jean Bourgain, Hoai-Minh Nguyen. 2006
115 citations recorded by the source corpus.
Our main result is the following: Let g∈Lp(RN), 1<p<+∞, be such that supn∈N∫RN∫RN|g(x)−g(y)|>δnδnp|x−y|N+pdxdy<+∞, for some arbitrary sequence of positive numbers (δn)n∈N with limn→∞δn=0. Then g∈W1,p(RN). This extends a result from H.-M. Nguyen (2006). To cite this article: J. Bourgain, H.-M. Nguyen, C. R. Acad. Sci. Paris, Ser. I 343 (2006).
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/2c378a3fec201ce443fc3ed9e219cb42dcbe276a
How researchers see this paper
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In Applied Mathematics
- Nicola Gigli
- Hoai-Minh Nguyen
- Luigi Ambrosio
- Andrea Mondino
- Giuseppe Savar'e
- Elia Brué
- Filippo Santambrogio
- Fabio Cavalletti
In Numerical Analysis
Citations in the corpus
- Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below (2014, methodology): “To the best of our knowledge, attempts to define higher order Sobolev spaces on metric measure spaces have been done only in [39] and [1].”
- Some new characterizations of Sobolev spaces (2006, background): “The answer is positive but the argument is completely different and much more delicate (see [ 2 ]).”