Alessio Figalli's Books

Partial Differential Equations and Geometric Measure Theory

Cetraro, Italy 2014

By: Alessio Figalli,Enrico Valdinoci,Ireneo Peral

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Partial Differential Equations and Geometric Measure Theory

Cetraro, Italy 2014

By: Alessio Figalli,Enrico Valdinoci,Ireneo Peral

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

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Page Count

224

Publisher

Springer

Published Date

ISBN 10

3319740423

ISBN 13

9783319740423

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Cetraro, Italy 2016

By: José Antonio Carrillo,Manuel del Pino,Alessio Figalli,Giuseppe Mingione,Juan Luis Vázquez

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Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Cetraro, Italy 2016

By: José Antonio Carrillo,Manuel del Pino,Alessio Figalli,Giuseppe Mingione,Juan Luis Vázquez

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.

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Page Count

288

Publisher

Springer

Published Date

ISBN 10

3319614940

ISBN 13

9783319614946

Mean Field Games

Cetraro, Italy 2019

By: Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio

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Mean Field Games

Cetraro, Italy 2019

By: Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio

This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.

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Page Count

316

Publisher

Springer Nature

Published Date

ISBN 10

3030598373

ISBN 13

9783030598372

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Cetraro, Italy 2016

By: José Antonio Carrillo,Manuel del Pino,Alessio Figalli,Giuseppe Mingione,Juan Luis Vázquez

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Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Cetraro, Italy 2016

By: José Antonio Carrillo,Manuel del Pino,Alessio Figalli,Giuseppe Mingione,Juan Luis Vázquez

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Page Count

288

Publisher

Springer

Published Date

ISBN 10

3319614940

ISBN 13

9783319614946

Partial Differential Equations and Geometric Measure Theory

Cetraro, Italy 2014

By: Alessio Figalli,Enrico Valdinoci,Ireneo Peral

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Partial Differential Equations and Geometric Measure Theory

Cetraro, Italy 2014

By: Alessio Figalli,Enrico Valdinoci,Ireneo Peral

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Page Count

224

Publisher

Springer

Published Date

ISBN 10

3319740423

ISBN 13

9783319740423

The Monge-Ampère Equation and Its Applications

By: Alessio Figalli

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The Monge-Ampère Equation and Its Applications

By: Alessio Figalli

The Monge-Ampère equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry. This monograph is a comprehensive introduction to the existence and regularity theory of the Monge-Ampère equation and some selected applications; the main goal is to provide the reader with a wealth of results and techniques he or she can draw from to understand current research related to this beautiful equation. The presentation is essentially self-contained, with an appendix wherein one can find precise statements of all the results used from different areas (linear algebra, convex geometry, measure theory, nonlinear analysis, and PDEs). This book is intended for graduate students and researchers interested in nonlinear PDEs: explanatory figures, detailed proofs, and heuristic arguments make this book suitable for self-study and also as a reference.

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Page Count

210

Published Date

ISBN 10

303719670X

ISBN 13

9783037196700

Book's by Alessio Figalli

Partial Differential Equations and Geometric Measure Theory

Partial Differential Equations and Geometric Measure Theory

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Mean Field Games

Mean Field Games

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

Partial Differential Equations and Geometric Measure Theory

Partial Differential Equations and Geometric Measure Theory

The Monge-Ampère Equation and Its Applications

The Monge-Ampère Equation and Its Applications

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