{"product_id":"optimal-mass-transport-on-euclidean-spaces-hardback-9781009179706","title":"Optimal Mass Transport on Euclidean Spaces (Hardback) 9781009179706","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eOptimal Mass Transport on Euclidean Spaces\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eFrancesco Maggi (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009179706, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 16 November 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e316 pages\u003cbr\u003e23.5 x 15.9 x 2.5 cm, 0.63 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'The author brings original and pedagogical ideas and illuminating remarks to his presentation, so his book is absolutely worth working with for teaching, solo learning, reading groups and research … Francesco Maggi's book can be recommended to anybody interested in the topic.' Nicolas Juillet, MathSciNet\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eOptimal mass transport has emerged in the past three decades as an active field with wide-ranging connections to the calculus of variations, PDEs, and geometric analysis. This graduate-level introduction covers the field's theoretical foundation and key ideas in applications. By focusing on optimal mass transport problems in a Euclidean setting, the book is able to introduce concepts in a gradual, accessible way with minimal prerequisites, while remaining technically and conceptually complete. Working in a familiar context will help readers build geometric intuition quickly and give them a strong foundation in the subject. This book explores the relation between the Monge and Kantorovich transport problems, solving the former for both the linear transport cost (which is important in geometric applications) and for the quadratic transport cost (which is central in PDE applications), starting from the solution of the latter for arbitrary transport costs.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Notation\u003cbr\u003e Part I. The Kantorovich Problem: 1. An introduction to the Monge problem\u003cbr\u003e 2. Discrete transport problems\u003cbr\u003e 3. The Kantorovich problem\u003cbr\u003e Part II. Solution of the Monge Problem with Quadratic Cost: the Brenier-McCann Theorem: 4. The Brenier theorem\u003cbr\u003e 5. First order differentiability of convex functions\u003cbr\u003e 6. The Brenier-McCann theorem\u003cbr\u003e 7. Second order differentiability of convex functions\u003cbr\u003e 8. The Monge-Ampère equation for Brenier maps\u003cbr\u003e Part III. Applications to PDE and the Calculus of Variations and the Wasserstein Space: 9. Isoperimetric and Sobolev inequalities in sharp form\u003cbr\u003e 10. Displacement convexity and equilibrium of gases\u003cbr\u003e 11. The Wasserstein distance W2 on P2(Rn)\u003cbr\u003e 12. Gradient flows and the minimizing movements scheme\u003cbr\u003e 13. The Fokker-Planck equation in the Wasserstein space\u003cbr\u003e 14. The Euler equations and isochoric projections\u003cbr\u003e 15. Action minimization, Eulerian velocities and Otto's calculus\u003cbr\u003e Part IV. Solution of the Monge Problem with Linear Cost: the Sudakov Theorem: 16. Optimal transport maps on the real line\u003cbr\u003e 17. Disintegration\u003cbr\u003e 18. Solution to the Monge problem with linear cost\u003cbr\u003e 19. An introduction to the needle decomposition method\u003cbr\u003e Appendix A: Radon measures on Rn and related topics\u003cbr\u003e Appendix B: Bibliographical Notes\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52470043083032,"sku":"9781009179706","price":43.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009179706i.jpg?v=1785629580","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/optimal-mass-transport-on-euclidean-spaces-hardback-9781009179706","provider":"Freshly Printed Books","version":"1.0","type":"link"}