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Functions of Bounded Variation and Free Discontinuity Problems
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 continuityExpand
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Gradient Flows: In Metric Spaces and in the Space of Probability Measures
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 ConvergenceExpand
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Currents in metric spaces
C o n t e n t s Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ] 1. Notation and preliminary results . . . . . . . . . . . . . . . . . . . . 7 2. Metric functionals .Expand
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Approximation of functional depending on jumps by elliptic functional via t-convergence
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 functionalsExpand
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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 theirExpand
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Lecture Notes on Optimal Transport Problems
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 ofExpand
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Metric measure spaces with Riemannian Ricci curvature bounded from below
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 FinslerExpand
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A User’s Guide to Optimal Transport
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 optimalExpand
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Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
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 generalExpand
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