[图书][B] Functions of bounded variation and free discontinuity problems

L Ambrosio, N Fusco, D Pallara - 2000 - academic.oup.com
This book deals with a class of mathematical problems which involve the minimization of the
sum of a volume and a surface energy and have lately been refered to as' free discontinuity …

[图书][B] Variational analysis in Sobolev and BV spaces: applications to PDEs and optimization

H Attouch, G Buttazzo, G Michaille - 2014 - SIAM
This second edition takes advantage of several comments received by colleagues and
students. With respect to the first edition (published by SIAM in 2006) several new sections …

Transport equation and Cauchy problem forBVvector fields.

L Ambrosio - Inventiones mathematicae, 2004 - search.ebscohost.com
Transport equation and Cauchy problem for BV vector fields Page 1 DOI: 10.1007/s00222-004-0367-2
Invent. math. 158, 227–260 (2004) Transport equation and Cauchy problem for BV vector …

On the structure of 𝓐-free measures and applications

G De Philippis, F Rindler - Annals of Mathematics, 2016 - JSTOR
We establish a general structure theorem for the singular part of 𝓐-free Radon measures,
where 𝓐 is a linear PDE operator. By applying the theorem to suitably chosen differential …

Transport equation and Cauchy problem for non-smooth vector fields

L Ambrosio, L Caffarelli, MG Crandall, LC Evans… - Calculus of Variations …, 2008 - Springer
Transport Equation and Cauchy Problem for Non-Smooth Vector Fields Page 1 Transport
Equation and Cauchy Problem for Non-Smooth Vector Fields Luigi Ambrosio Scuola Normale …

[图书][B] Calculus of variations

F Rindler - 2018 - Springer
The calculus of variations has its roots in the first problems of optimality studied in classical
antiquity by Archimedes (ca. 287–212 BC in Syracuse, Magna Graecia) and Zenodorus (ca …

Continuity equations and ODE flows with non-smooth velocity

L Ambrosio, G Crippa - Proceedings of the Royal Society of …, 2014 - cambridge.org
In this paper we review many aspects of the well-posedness theory for the Cauchy problem
for the continuity and transport equations and for the ordinary differential equation (ODE). In …

[PDF][PDF] Relaxation of quasiconvex functionals in BV (, Rp) for integrands f (x, u,∇ u)

I Fonseca, S Müller - Arch. Ration. Mech. Anal, 1993 - kilthub.cmu.edu
In this paper it is shown that if f (x, u,.) is a quasiconvex function with linear growth then the
relaxed functional in u-> ff (x, u (x), Vu (x» dx with respect to the L1 topology has an integral …

A geometrical approach to monotone functions in

G Alberti, L Ambrosio - Mathematische Zeitschrift, 1999 - Springer
The paper is concerned with the fine properties of monotone functions on R^n. We study the
continuity and differentiability properties of these functions, the approximability properties …

Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields

L Ambrosio, G Crippa, C De Lellis, F Otto… - Transport equations and …, 2008 - Springer
In these notes we discuss some recent progress on the problem of the existence,
uniqueness and stability of the flow associated to a weakly differentiable (Sobolev or BV …