Luis A. Caffarelli's Books

A Geometric Approach to Free Boundary Problems

By: Luis A. Caffarelli,S. Salsa

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A Geometric Approach to Free Boundary Problems

By: Luis A. Caffarelli,S. Salsa

We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.

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Page Count

282

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821837842

ISBN 13

9780821837849

Fully Nonlinear Elliptic Equations

By: Luis A. Caffarelli,Xavier Cabré

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Fully Nonlinear Elliptic Equations

By: Luis A. Caffarelli,Xavier Cabré

The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

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Page Count

114

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821804375

ISBN 13

9780821804377

Nonlinear Partial Differential Equations

By: Luis A. Caffarelli,François Golse,Yan Guo,Carlos E. Kenig,Alexis Vasseur

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Nonlinear Partial Differential Equations

By: Luis A. Caffarelli,François Golse,Yan Guo,Carlos E. Kenig,Alexis Vasseur

The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles.

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Page Count

156

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034801912

ISBN 13

9783034801911

Calculus of Variations and Nonlinear Partial Differential Equations

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005

By: Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco

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Calculus of Variations and Nonlinear Partial Differential Equations

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005

By: Luigi Ambrosio,Luis A. Caffarelli,Michael G. Crandall,Lawrence C. Evans,Nicola Fusco

This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

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213

Publisher

Springer

Published Date

ISBN 10

354075914X

ISBN 13

9783540759140

Monge Ampere Equation: Applications to Geometry and Optimization

Applications to Geometry and Optimization : NSF-CBMS Conference on the Monge Ampère Equation, Applications to Geometry and Optimization, July 9-13, 1997, Florida Atlantic University

By: Luis A. Caffarelli,Mario Milman

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Monge Ampere Equation: Applications to Geometry and Optimization

Applications to Geometry and Optimization : NSF-CBMS Conference on the Monge Ampère Equation, Applications to Geometry and Optimization, July 9-13, 1997, Florida Atlantic University

By: Luis A. Caffarelli,Mario Milman

In recent years, the Monge Ampère Equation has received attention for its role in several new areas of applied mathematics: as a new method of discretization for evolution equations of classical mechanics, such as the Euler equation, flow in porous media, Hele-Shaw flow, etc.; as a simple model for optimal transportation and a div-curl decomposition with affine invariance; and as a model for front formation in meteorology and optimal antenna design. These applications were addressed and important theoretical advances presented at a NSF-CBMS conference held at Florida Atlantic University (Boca Raton). L. Cafarelli and other distinguished specialists contributed high-quality research results and up-to-date developments in the field. This is a comprehensive volume outlining current directions in nonlinear analysis and its applications.

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Page Count

186

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821809172

ISBN 13

9780821809174

Optimal Transportation and Applications

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2–8, 2001

By: Luigi Ambrosio,Luis A. Caffarelli,Yann Brenier,Giuseppe Buttazzo,Cédric Villani

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Optimal Transportation and Applications

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2–8, 2001

By: Luigi Ambrosio,Luis A. Caffarelli,Yann Brenier,Giuseppe Buttazzo,Cédric Villani

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.

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Page Count

176

Publisher

Springer

Published Date

ISBN 10

3540448578

ISBN 13

9783540448570

Hyperbolic Equations and Frequency Interactions

By: Luis A. Caffarelli,Weinan E

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Hyperbolic Equations and Frequency Interactions

By: Luis A. Caffarelli,Weinan E

The research topic for this IAS/PCMS Summer Session was nonlinear wave phenomena. Mathematicians from the more theoretical areas of PDEs were brought together with those involved in applications. The goal was to share ideas, knowledge, and perspectives. How waves, or "frequencies", interact in nonlinear phenomena has been a central issue in many of the recent developments in pure and applied analysis. It is believed that wavelet theory--with its simultaneous localization in both physical and frequency space and its lacunarity--is and will be a fundamental new tool in the treatment of the phenomena. Included in this volume are write-ups of the "general methods and tools" courses held by Jeff Rauch and Ingrid Daubechies. Rauch's article discusses geometric optics as an asymptotic limit of high-frequency phenomena. He shows how nonlinear effects are reflected in the asymptotic theory. In the article "Harmonic Analysis, Wavelets and Applications" by Daubechies and Gilbert the main structure of the wavelet theory is presented. Also included are articles on the more "specialized" courses that were presented, such as "Nonlinear Schrödinger Equations" by Jean Bourgain and "Waves and Transport" by George Papanicolaou and Leonid Ryzhik. Susan Friedlander provides a written version of her lecture series "Stability and Instability of an Ideal Fluid", given at the Mentoring Program for Women in Mathematics, a preliminary program to the Summer Session. This Summer Session brought together students, fellows, and established mathematicians from all over the globe to share ideas in a vibrant and exciting atmosphere. This book presents the compelling results. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

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Page Count

480

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821805924

ISBN 13

9780821805923

Book's by Luis A. Caffarelli

A Geometric Approach to Free Boundary Problems

A Geometric Approach to Free Boundary Problems

Fully Nonlinear Elliptic Equations

Fully Nonlinear Elliptic Equations

Nonlinear Partial Differential Equations

Nonlinear Partial Differential Equations

Calculus of Variations and Nonlinear Partial Differential Equations

Calculus of Variations and Nonlinear Partial Differential Equations

Monge Ampere Equation: Applications to Geometry and Optimization

Monge Ampere Equation: Applications to Geometry and Optimization

Optimal Transportation and Applications

Optimal Transportation and Applications

Hyperbolic Equations and Frequency Interactions

Hyperbolic Equations and Frequency Interactions

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