Failure of the chain rule for the divergence of bounded vector fields
Crippa G, Gusev N, Spirito S, Wiedemann E (2017)
Publication Type: Journal article
Publication year: 2017
Journal
Book Volume: 17
Pages Range: 1-18
Journal Issue: 1
DOI: 10.2422/2036-2145.201506_006
Abstract
We provide a vast class of counterexamples to the chain rule for the divergence of bounded vector fields in three space dimensions. Our convex integration approach allows us to produce renormalization defects of various kinds, which in a sense quantify the breakdown of the chain rule. For instance, we can construct defects which are absolutely continuous with respect to the Lebesgue measure, or defects which are not even measures.
Authors with CRIS profile
Involved external institutions
Universität Basel
Switzerland (CH)
Steklov Mathematical Institute
Russian Federation (RU)
University of L'Aquila / Università degli Studi dell'Aquila
Italy (IT)
Gottfried Wilhelm Leibniz Universität Hannover
Germany (DE)
Switzerland (CH)
Steklov Mathematical Institute
Russian Federation (RU)
University of L'Aquila / Università degli Studi dell'Aquila
Italy (IT)
Gottfried Wilhelm Leibniz Universität Hannover
Germany (DE)
How to cite
APA:
Crippa, G., Gusev, N., Spirito, S., & Wiedemann, E. (2017). Failure of the chain rule for the divergence of bounded vector fields. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 17(1), 1-18. https://dx.doi.org/10.2422/2036-2145.201506_006
MLA:
Crippa, Gianluca, et al. "Failure of the chain rule for the divergence of bounded vector fields." Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 17.1 (2017): 1-18.
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