An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields
Title An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields PDF eBook
Author Marco Bramanti
Publisher Springer Science & Business Media
Pages 157
Release 2013-11-20
Genre Mathematics
ISBN 3319020870

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​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.

An Invitation to Hypoelliptic Operators and Hormander's Vector Fields

An Invitation to Hypoelliptic Operators and Hormander's Vector Fields
Title An Invitation to Hypoelliptic Operators and Hormander's Vector Fields PDF eBook
Author Marco Bramanti
Publisher
Pages 164
Release 2013-11-30
Genre
ISBN 9783319020884

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Hormander Operators

Hormander Operators
Title Hormander Operators PDF eBook
Author Marco Bramanti
Publisher World Scientific
Pages 722
Release 2022-10-21
Genre Mathematics
ISBN 9811261709

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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.

Maximal Subellipticity

Maximal Subellipticity
Title Maximal Subellipticity PDF eBook
Author Brian Street
Publisher Walter de Gruyter GmbH & Co KG
Pages 768
Release 2023-07-03
Genre Mathematics
ISBN 3111085643

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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.

An Introduction To The Geometrical Analysis Of Vector Fields: With Applications To Maximum Principles And Lie Groups

An Introduction To The Geometrical Analysis Of Vector Fields: With Applications To Maximum Principles And Lie Groups
Title An Introduction To The Geometrical Analysis Of Vector Fields: With Applications To Maximum Principles And Lie Groups PDF eBook
Author Stefano Biagi
Publisher World Scientific
Pages 450
Release 2018-12-05
Genre Mathematics
ISBN 9813276630

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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:

Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations

Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations
Title Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations PDF eBook
Author Camille Laurent
Publisher American Mathematical Society
Pages 108
Release 2022-04-08
Genre Mathematics
ISBN 1470451387

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New Trends on Analysis and Geometry in Metric Spaces

New Trends on Analysis and Geometry in Metric Spaces
Title New Trends on Analysis and Geometry in Metric Spaces PDF eBook
Author Fabrice Baudoin
Publisher Springer Nature
Pages 312
Release 2022-02-04
Genre Mathematics
ISBN 3030841413

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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.