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

Annali della Scuola Normale Superiore di Pisa-Classe di Scienze

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

Emil Wiedemann

Involved external institutions

Universität Basel CH Switzerland (CH) Steklov Mathematical Institute RU Russian Federation (RU) University of L'Aquila / Università degli Studi dell'Aquila IT Italy (IT) Gottfried Wilhelm Leibniz Universität Hannover DE 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://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.

BibTeX: Download