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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
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
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
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
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
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
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