Authors:
- 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
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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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.
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)
Authors and Affiliations
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Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
Marco Bramanti
About the author
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".
Bibliographic Information
Book Title: An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields
Authors: Marco Bramanti
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-02087-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2014
Softcover ISBN: 978-3-319-02086-0Published: 05 December 2013
eBook ISBN: 978-3-319-02087-7Published: 20 November 2013
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XI, 150
Number of Illustrations: 3 b/w illustrations
Topics: Partial Differential Equations, Analysis, Operator Theory