An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields PDF Download
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Author: Marco Bramanti
Publisher: Springer Science & Business Media
ISBN: 3319020870
Category : Mathematics
Languages : en
Pages : 157
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Book Description
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.
Author: Marco Bramanti
Publisher: Springer Science & Business Media
ISBN: 3319020870
Category : Mathematics
Languages : en
Pages : 157
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Book Description
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.
Author: Marco Bramanti
Publisher:
ISBN: 9783319020884
Category :
Languages : en
Pages : 164
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Book Description
Author: Marco Bramanti
Publisher: World Scientific
ISBN: 9811261709
Category : Mathematics
Languages : en
Pages : 722
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Book Description
Hörmander operators are a class of linear second order partial differential operators with nonnegative characteristic form and smooth coefficients, which are usually degenerate elliptic-parabolic, but nevertheless hypoelliptic, that is highly regularizing. The study of these operators began with the 1967 fundamental paper by Lars Hörmander and is intimately connected to the geometry of vector fields.Motivations for the study of Hörmander operators come for instance from Kolmogorov-Fokker-Planck equations arising from modeling physical systems governed by stochastic equations and the geometric theory of several complex variables. The aim of this book is to give a systematic exposition of a relevant part of the theory of Hörmander operators and vector fields, together with the necessary background and prerequisites.The book is intended for self-study, or as a reference book, and can be useful to both younger and senior researchers, already working in this area or aiming to approach it.
Author: Brian Street
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111085643
Category : Mathematics
Languages : en
Pages : 768
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Book Description
Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.
Author: Stefano Biagi
Publisher: World Scientific
ISBN: 9813276630
Category : Mathematics
Languages : en
Pages : 450
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Book Description
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
Author: Camille Laurent
Publisher: American Mathematical Society
ISBN: 1470451387
Category : Mathematics
Languages : en
Pages : 108
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Book Description
View the abstract.
Author: Fabrice Baudoin
Publisher: Springer Nature
ISBN: 3030841413
Category : Mathematics
Languages : en
Pages : 312
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Book Description
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.
Author: Adrian Constantin
Publisher: Cambridge University Press
ISBN: 1316670805
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.
Author: Adrian Constantin
Publisher: Cambridge University Press
ISBN: 1107044103
Category : Mathematics
Languages : en
Pages : 368
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Book Description
A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.
Author: Andrei Agrachev
Publisher: Cambridge University Press
ISBN: 110847635X
Category : Mathematics
Languages : en
Pages : 765
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Book Description
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
