edoc

Failure of the chain rule for the divergence of bounded vector fields

Crippa, Gianluca and Gusev, Nikolay and Spirito, Stefano and Wiedemann, Emil. (2017) Failure of the chain rule for the divergence of bounded vector fields. Annali della Scuola Normale di Pisa - Classe di Scienze, 17 (1). pp. 1-18.

[img]
Preview
PDF - Accepted Version
288Kb

Official URL: http://edoc.unibas.ch/40182/

Downloads: Statistics Overview

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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Scuola Normale Superiore, Pisa
ISSN:0391-173X
e-ISSN:2036-2145
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:25 May 2018 13:12
Deposited On:21 Aug 2017 12:31

Repository Staff Only: item control page