Giuseppe Savare's Books

New Trends on Analysis and Geometry in Metric Spaces

Levico Terme, Italy 2017

By: Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam

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New Trends on Analysis and Geometry in Metric Spaces

Levico Terme, Italy 2017

By: Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.

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Page Count

312

Publisher

Springer Nature

Published Date

ISBN 10

3030841413

ISBN 13

9783030841416

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

By: Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré

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Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

By: Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré

The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.

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Page Count

134

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470439131

ISBN 13

9781470439132

Gradient Flows

In Metric Spaces and in the Space of Probability Measures

By: Luigi Ambrosio,Nicola Gigli,Giuseppe Savare

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Gradient Flows

In Metric Spaces and in the Space of Probability Measures

By: Luigi Ambrosio,Nicola Gigli,Giuseppe Savare

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

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Page Count

333

Publisher

Springer Science & Business Media

Published Date

ISBN 10

376438722X

ISBN 13

9783764387228

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

Gradient Flows

In Metric Spaces and in the Space of Probability Measures

By: Luigi Ambrosio,Nicola Gigli,Giuseppe Savare

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Gradient Flows

In Metric Spaces and in the Space of Probability Measures

By: Luigi Ambrosio,Nicola Gigli,Giuseppe Savare

This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.

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Page Count

330

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764373091

ISBN 13

9783764373092

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

By: Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré

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Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

By: Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré

Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X, d, m). On the geometric side, our new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, our new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD*(K, N) condition of Bacher-Sturm.

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Page Count

121

Published Date

ISBN 10

1470455145

ISBN 13

9781470455149

New Trends on Analysis and Geometry in Metric Spaces

Levico Terme, Italy 2017

By: Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam

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New Trends on Analysis and Geometry in Metric Spaces

Levico Terme, Italy 2017

By: Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam

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Write a review

Solve jigsaw puzzle

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Page Count

312

Publisher

Springer Nature

Published Date

ISBN 10

3030841413

ISBN 13

9783030841416

Book's by Giuseppe Savare

New Trends on Analysis and Geometry in Metric Spaces

New Trends on Analysis and Geometry in Metric Spaces

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Gradient Flows

Gradient Flows

Optimal Transportation and Applications

Optimal Transportation and Applications

Gradient Flows

Gradient Flows

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

New Trends on Analysis and Geometry in Metric Spaces

New Trends on Analysis and Geometry in Metric Spaces

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