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Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions]


De Lellis, C (2008). Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions]. Astérisque, (317):175-204.

Abstract

In a seminal paper of almost 20 years ago, R.J. DiPerna and P.-L. Lions initiated the theory of renormalized solutions to study the well-posedness of Ordinary Differential Equations and Transport Equations with discontinuous coefficients. In a recent work L. Ambrosio solved the long-standing open problem of extending this theory to BV coefficients, the most common functional-analytic closure of classical functions with jump discontinuities.

Besides its intrinsic interest, Ambrosio's Theorem has been used to solve relevant problems in Partial Differential Equations and it opened the way to a series of new questions.

Abstract

In a seminal paper of almost 20 years ago, R.J. DiPerna and P.-L. Lions initiated the theory of renormalized solutions to study the well-posedness of Ordinary Differential Equations and Transport Equations with discontinuous coefficients. In a recent work L. Ambrosio solved the long-standing open problem of extending this theory to BV coefficients, the most common functional-analytic closure of classical functions with jump discontinuities.

Besides its intrinsic interest, Ambrosio's Theorem has been used to solve relevant problems in Partial Differential Equations and it opened the way to a series of new questions.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:09 Nov 2009 01:12
Last Modified:05 Apr 2016 13:23
Publisher:Société mathématique de France (SMF)
ISSN:0303-1179
ISBN:978-2-85629-253-2
Additional Information:Séminaire Bourbaki. Vol. 2006/2007; Ex No. 972, viii, 175
Official URL:http://smf.emath.fr/Publications/Asterisque/2008/317/html/smf_ast_317_175-204.html

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