Fundamental Solutions And Local Solvability For Nonsmooth Hormander S Operators
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Fundamental Solutions And Local Solvability For Nonsmooth Hormander S Operators
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Author : Marco Bramanti
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-25
Fundamental Solutions And Local Solvability For Nonsmooth Hormander S Operators written by Marco Bramanti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Mathematics categories.
The authors consider operators of the form in a bounded domain of where are nonsmooth Hörmander's vector fields of step such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution for and provide growth estimates for and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that also possesses second derivatives, and they deduce the local solvability of , constructing, by means of , a solution to with Hölder continuous . The authors also prove estimates on this solution.
Geometric Methods In Pde S
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Author : Giovanna Citti
language : en
Publisher: Springer
Release Date : 2015-10-31
Geometric Methods In Pde S written by Giovanna Citti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-31 with Mathematics categories.
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.
An Invitation To Hypoelliptic Operators And H Rmander S Vector Fields
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Author : Marco Bramanti
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-20
An Invitation To Hypoelliptic Operators And H Rmander S Vector Fields written by Marco Bramanti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-20 with Mathematics categories.
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.
Hardy Inequalities On Homogeneous Groups
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Author : Michael Ruzhansky
language : en
Publisher: Springer
Release Date : 2019-07-02
Hardy Inequalities On Homogeneous Groups written by Michael Ruzhansky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-02 with Mathematics categories.
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
Elementary Introduction To The Theory Of Pseudodifferential Operators
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Author : Xavier Saint Raymond
language : en
Publisher: Routledge
Release Date : 2018-02-06
Elementary Introduction To The Theory Of Pseudodifferential Operators written by Xavier Saint Raymond and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-06 with Mathematics categories.
In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.
Partial Differential Equations In Several Complex Variables
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Author : So-chin Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Partial Differential Equations In Several Complex Variables written by So-chin Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.
Pseudodifferential Operators Pms 34
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Author : Michael Eugene Taylor
language : en
Publisher: Princeton University Press
Release Date : 2017-03-14
Pseudodifferential Operators Pms 34 written by Michael Eugene Taylor and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-14 with Mathematics categories.
Here Michael Taylor develops pseudodifferential operators as a tool for treating problems in linear partial differential equations, including existence, uniqueness, and estimates of smoothness, as well as other qualitative properties. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Anomalies In Partial Differential Equations
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Author : Massimo Cicognani
language : en
Publisher: Springer Nature
Release Date : 2021-02-03
Anomalies In Partial Differential Equations written by Massimo Cicognani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-03 with Mathematics categories.
The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in the action of localizing operators or the description of wave front sets, complete the volume.
Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards
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Author :
language : en
Publisher:
Release Date : 1986
Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Dissertations, Academic categories.