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1. Introduction to Measure Theory and Integration
by Luigi Ambrosio, Giuseppe Prato, Andrea Mennucci
出版情報: Pisa : Edizioni della Normale, 2011
シリーズ名: Appunti/Lecture Notes ; 10
オンライン: http://dx.doi.org/10.1007/978-88-7642-386-4
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2. Transport Equations and Multi-D Hyperbolic Conservation Laws
by Luigi Ambrosio, Gianluca Crippa, Camillo Lellis, Felix Otto, Michael Westdickenberg
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2008
シリーズ名: Lecture Notes of the Unione Matematica Italiana ; 5
オンライン: http://dx.doi.org/10.1007/978-3-540-76781-7
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3. Gradient Flows : in Metric Spaces and in the Space of Probability Measures. Second Edition
by Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré ; edited by Michael Struwe
出版情報: Basel : Birkhäuser Basel, 2008
シリーズ名: Lectures in Mathematics ETH Zürich ;
オンライン: http://dx.doi.org/10.1007/978-3-7643-8722-8
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4. Geometric Measure Theory and Real Analysis
edited by Luigi Ambrosio
出版情報: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2014
シリーズ名: Publications of the Scuola Normale Superiore ; 17
オンライン: http://dx.doi.org/10.1007/978-88-7642-523-3
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目次情報: 続きを見る
Vladimir I. Bogachev: Sobolev classes on infinite-dimensional spaces
Roberto Monti: Isoperimetric problem and minimal surfaces in the Heisenberg group
Emanuele Spadaro: Regularity of higher codimension area minimizing integral currents
Davide Vittone: The regularity problem for sub-Riemannian geodesics
Vladimir I. Bogachev: Sobolev classes on infinite-dimensional spaces
Roberto Monti: Isoperimetric problem and minimal surfaces in the Heisenberg group
Emanuele Spadaro: Regularity of higher codimension area minimizing integral currents
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5. Ennio De Giorgi: Selected Papers
edited by Luigi AmbrosioGianni Dal Maso, Marco Forti, Mario Miranda et al
出版情報: Berlin Heidelberg : Springer-Verlag GmbH., 2006
オンライン: http://dx.doi.org/10.1007/3-540-33983-3
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6. Calculus of Variations and Nonlinear Partial Differential Equations : With a historical overview by Elvira Mascolo
by Luigi Ambrosio, Luis Caffarelli, Michael G. Crandall, Lawrence C. Evans, Nicola Fusco ; edited by Bernard Dacorogna, Paolo Marcellini
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2008
シリーズ名: Lecture Notes in Mathematics ; 1927
オンライン: http://dx.doi.org/10.1007/978-3-540-75914-0
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7. Modelling and Optimisation of Flows on Networks : Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle
by Luigi Ambrosio, Alberto Bressan, Dirk Helbing, Axel Klar, Enrique Zuazua
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
シリーズ名: Lecture Notes in Mathematics ; 2062
オンライン: http://dx.doi.org/10.1007/978-3-642-32160-3
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目次情報: 続きを見る
A User’s Guide to Optimal Transport
Hyperbolic Conservation Laws: an Illustrated Tutorial
Derivation of Non-Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models
On the Controversy around Daganzo’s Requiem for and Aw-Rascle’s Resurrection of Second-Order Traffic Flow Models
Theoretical vs. Empirical Classification and Prediction of Congested Traffic States
Self-Organized Network Flows
Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections
Modeling and Optimization of Scalar Flows on Networks
The Wave Equation: Control and Numerics
A User’s Guide to Optimal Transport
Hyperbolic Conservation Laws: an Illustrated Tutorial
Derivation of Non-Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models
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8. Lectures on Optimal Transport. 1st ed. 2021
by Luigi Ambrosio, Elia Brué, Daniele Semola
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: La Matematica per il 3+2 ; 130
オンライン: https://doi.org/10.1007/978-3-030-72162-6
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目次情報: 続きを見る
1 Lecture 1: Preliminary notions and the Monge problem
2 Lecture 2: The Kantorovich problem
3 Lecture 3: The Kantorovich - Rubinstein duality
4 Lecture 4: Necessary and sufficient optimality conditions
5 Lecture 5: Existence of optimal maps and applications
6 Lecture 6: A proof of the Isoperimetric inequality and stability in Optimal Transport
7 Lecture 7: The Monge-Ampére equation and Optimal Transport on Riemannian manifolds
8 Lecture 8: The metric side of Optimal Transport
9 Lecture 9: Analysis on metric spaces and the dynamic formulation of Optimal Transport
10 Lecture 10: Wasserstein geodesics, nonbranching and curvature
11 Lecture 11: Gradient flows: an introduction
12 Lecture 12: Gradient flows: the Brézis-Komura theorem
13 Lecture 13: Examples of gradient flows in PDEs
14 Lecture 14: Gradient flows: the EDE and EDI formulations
15 Lecture 15: Semicontinuity and convexity of energies in the Wasserstein space
16 Lecture 16: The Continuity Equation and the Hopf-Lax semigroup
17 Lecture 17: The Benamou-Brenier formula
18 Lecture 18: An introduction to Otto’s calculus
19 Lecture 19: Heat flow, Optimal Transport and Ricci curvature
1 Lecture 1: Preliminary notions and the Monge problem
2 Lecture 2: The Kantorovich problem
3 Lecture 3: The Kantorovich - Rubinstein duality
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9. New Trends on Analysis and Geometry in Metric Spaces : Levico Terme, Italy 2017. 1st ed. 2022
by Fabrice Baudoin, Séverine Rigot, Giuseppe Savaré, Nageswari Shanmugalingam ; edited by Luigi Ambrosio, Bruno Franchi, Irina Markina, Francesco Serra Cassano
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2022
シリーズ名: C.I.M.E. Foundation Subseries ; 2296
オンライン: https://doi.org/10.1007/978-3-030-84141-6
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