Optimal Transport and Applications to Geom...

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Beschreibung

This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area.

Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.

Über den Autor

Dr. Cristian E. Gutierrez is a Professor at Temple University. His research areas include partial differential equations, geometric optics, optimal transport, and electromagnetism. He is a Fellow of the American Mathematical Society, a Member of the Academy of Sciences of Argentina, and a Member of the Academy of Sciences of the University of Bologna, Italy.

Zusammenfassung

Explores the connection between optimal transport and geometric optics, focusing on the design of free-form lenses

Offers self-contained presentation, with detailed explanations and full proofs of the theorems and results

Leverages optimal transport principles for the design of non-rotationally symmetric lenses

Inhaltsverzeichnis

Chapter 1 Introduction.- Chapter 2 The normal mapping or subdifferential.-Chapter 3 Sinkhorn's theorem and application to the distribution problem.- Chapter4 Monge-Kantorovich distance.- Chapter 5 Multivalued measure preserving maps.- Chapter 6 Kantorovich Dual Problem.- Chapter 7 Brenier and Aleksandrov solutions.- Chapter 8 Cyclical monotonicity.- Chapter 9 Quadratic cost.- Chapter 10 Brenier 's Polar Factorization Theorem.- Chapter 11 Benamou and Brenier formula.- Chapter 12 Snell's law of refraction.- Chapter 13 Solution of the far field refractor problem < 1.- Chapter 14 Proof of the Disintegration Theorem.- Chapter 15 Acknowledgements.- Chapter 16 References.

Details

Erscheinungsjahr:	2023
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	148
Reihe:	SpringerBriefs on PDEs and Data Science
Inhalt:	x 135 S. 1 s/w Illustr. 135 p. 1 illus.
ISBN-13:	9789819948666
ISBN-10:	9819948665
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Gutiérrez, Cristian E.
Auflage:	1st ed. 2023
Hersteller:	Springer Singapore Springer Nature Singapore SpringerBriefs on PDEs and Data Science
Maße:	235 x 155 x 9 mm
Von/Mit:	Cristian E. Gutiérrez
Erscheinungsdatum:	10.12.2023
Gewicht:	0,236 kg

preigu-id: 127178680