Gradient Flows

In Metric Spaces and in the Space of Probability Measures

Häftad, Engelska, 2008

Av Luigi Ambrosio, Nicola Gigli, Giuseppe Savare, Luigi Ambrosio, Nicola Gigli

1 679 kr

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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.

Produktinformation

Utgivningsdatum2008-03-13
Mått168 x 236 x 18 mm
Vikt681 g
FormatHäftad
SpråkEngelska
SerieLectures in Mathematics. ETH Zürich
Antal sidor334
Upplaga2
FörlagBirkhauser Verlag AG
ISBN9783764387211

Tillhör följande kategorier

Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the Convergence Theorems.- Uniqueness, Generation of Contraction Semigroups, Error Estimates.- Gradient Flow in the Space of Probability Measures.- Preliminary Results on Measure Theory.- The Optimal Transportation Problem.- The Wasserstein Distance and its Behaviour along Geodesics.- Absolutely Continuous Curves in p(X) and the Continuity Equation.- Convex Functionals in p(X).- Metric Slope and Subdifferential Calculus in (X).- Gradient Flows and Curves of Maximal Slope in p(X).