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Publications Influence

Functions of Bounded Variation and Free Discontinuity Problems

- L. Ambrosio, D. Pallara, N. Fusco
- Mathematics
- 2000

Measure Theory Basic Geometric Measure Theory Functions of bounded variation Special functions of bounded variation Semicontinuity in BV The Mumford-Shah functional Minimisers of free continuity… Expand

3,409 387- PDF

Gradient Flows: In Metric Spaces and in the Space of Probability Measures

- L. Ambrosio, Nicola Gigli, Giuseppe Savaré
- Mathematics
- 2005

Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the Convergence… Expand

2,327 345- PDF

Currents in metric spaces

- L. Ambrosio, Bernd Kirchheim
- Mathematics
- 8 March 2000

C o n t e n t s Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ] 1. Notation and preliminary results . . . . . . . . . . . . . . . . . . . . 7 2. Metric functionals .… Expand

339 80- PDF

Approximation of functional depending on jumps by elliptic functional via t-convergence

- L. Ambrosio, Vincenzo Maria Tortorelli
- Mathematics
- 1 December 1990

We show how it is possible to approximate the Mumford-Shah (see [29]) image segmentation functional
by elliptic functionals defined on Sobolev spaces. The heuristic idea is to consider functionals… Expand

903 54

Journal of materials science: materials in medicine.

- L. Ambrosio
- Medicine
- Journal of materials science. Materials in…
- 2003

▶ The Journal of Materials Science: Materials in Medicine carries a long tradition of publishing authoritative biomaterials research ▶ Covers the science and technology of biomaterials and their… Expand

505 44

Lecture Notes on Optimal Transport Problems

- L. Ambrosio
- Mathematics
- 2003

1 Some elementary examples
2 Optimal transport plans: existence and regularity
3 The one dimensional case
4 The ODE version of the optimal transport problem
5 The PDE version of… Expand

345 44

ON THE APPROXIMATION OF FREE DISCONTINUITY PROBLEMS

- L. Ambrosio, Vincenzo Maria Tortorelli
- Computer Science
- 1992

319 42

Metric measure spaces with Riemannian Ricci curvature bounded from below

- L. Ambrosio, Nicola Gigli, Giuseppe Savare'
- Mathematics
- 1 September 2011

In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence and rules out Finsler… Expand

353 28- PDF

A User’s Guide to Optimal Transport

- L. Ambrosio, Nicola Gigli
- Mathematics
- 2013

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal… Expand

273 27- PDF

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

- L. Ambrosio, Nicola Gigli, Giuseppe Savaré
- Mathematics
- 10 June 2011

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces $(X,\mathsf {d},\mathfrak {m})$. Our main results are: A general… Expand

287 27- PDF