The Flow Associated to Weakly Differentiable Vector Fields by Gianluca CrippaThe Flow Associated to Weakly Differentiable Vector Fields by Gianluca Crippa

The Flow Associated to Weakly Differentiable Vector Fields

byGianluca Crippa

Paperback | March 27, 2009

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The aim of this book is to provide a self-contained introduction and an up-to-date survey on many aspects of the theory of transport equations and ordinary differential equations with non-smooth velocity fields. The interest in this topic is motivated by important issues in nonlinear PDEs, in particular conservation laws and fluid mechanics. A fascinating feature of this research area, which is currently of concern in mathematics, is the interplay between PDE techniques and geometric measure theory techniques.Several masterpieces appear in the related literature, balancing completely rigorous proofs with more heuristic arguments. A consistent part of the book is based on results obtained by the author in collaboration with other mathematicians. After a short introduction to the classical smooth theory, the book is divided into two parts. The first part focuses on the PDE aspect of the problem, presenting some general tools of this analysis, many well-posedness results, an abstract characterization of the well-posedness, and some examples showing the sharpness of the assumptions made. The second part, instead, deals with the ODE aspect of the problem, respectively by an abstract connection with the PDE, and by some direct and simple (but powerful) a priori estimates.
Title:The Flow Associated to Weakly Differentiable Vector FieldsFormat:PaperbackDimensions:182 pages, 0.04 × 0.02 × 0 inPublished:March 27, 2009Publisher:Scuola Normale SuperioreLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:8876423400

ISBN - 13:9788876423406

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Editorial Reviews

From the reviews:"The monograph is very well written and I recommend it both to people working in the field and to everyone who would like to learn the basics of the theory."­­­ (Alessio Figalli, Mathematical Reviews, Issue 2010 k)