SpringerBriefs in Mathematics

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields

Authors: Bramanti, Marco

  • Introduces the fundamental ideas and discusses the classical results about Hörmander's operators
  • Provides the relevant motivations behind the research in this area, ranging on several different disciplines
  • Contains also an overview of the recent lines of research
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  • ISBN 978-3-319-02087-7
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About this book

​Hörmander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients, which have been intensively studied since the late 1960s and are still an active field of research. This text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development.

About the authors

Marco Bramanti is Associate Professor of Mathematical Analysis at the Department of Mathematics, Politecnico di Milano, Italy. Graduated in Mathematics in 1987, Ph.D. in Mathematics in 1993 at the University of Milano (Italy). He has been visiting University of Minnesota (USA) and Universidad Autnoma de Madrid (Spain). His current reasearch interests include linear second order partial differential equations with nonnegative characteristic form, geometry of ​Hörmander's vector fields, real analysis, in particular singular integral theory. Author of about 30 research papers on refereed journals, one research monograph, some contributions to congress proceedings, 14 textbooks, more than 60 reviews for "Mathematical Reviews".

Reviews

From the book reviews:

“It represents a detailed survey of the theory of hypoelliptic operators and Hörmander’s vector fields, containing all the main results, from the first contributions in the late 1960s up to the most recent results. … a valuable guide to the literature of this field and will certainly be much appreciated by every Ph.D. student working in PDEs.” (Fabio Nicola, Mathematical Reviews, February, 2015)

“The text is a good introduction to the subject for those interested in this branch of the theory of partial differential equations. … It has plenty of examples that illustrate the topics being studied, mainly in the first chapters. … The book finishes with some more recent results that are set, in some way, in an extended class of Hörmander’s operators.” (Sérgio Luís Zani, zbMATH, Vol. 1298, 2014)


Table of contents (5 chapters)

  • Hörmander’s Operators: What they are

    Bramanti, Marco

    Pages 1-14

  • Hörmander’s Operators: Why they are Studied

    Bramanti, Marco

    Pages 15-35

  • A Priori Estimates in Sobolev Spaces for Hörmander’s Operators

    Bramanti, Marco

    Pages 37-85

  • Geometry of Hörmander’s Vector Fields

    Bramanti, Marco

    Pages 87-117

  • Beyond Hörmander’s Operators

    Bramanti, Marco

    Pages 119-150

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-02087-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-02086-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-02087-7
DOI
10.1007/978-3-319-02087-7
Softcover ISBN
978-3-319-02086-0
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XI, 150
Number of Illustrations and Tables
3 b/w illustrations
Topics