Download or read book p Laplace Equation in the Heisenberg Group written by Diego Ricciotti and published by Springer. This book was released on 2015-12-28 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. In particular, it presents detailed proofs of smoothness for solutions to the non-degenerate equation and of Lipschitz regularity for solutions to the degenerate one. An introductory chapter presents the basic properties of the Heisenberg group, making the coverage self-contained. The setting is the first Heisenberg group, helping to keep the notation simple and allow the reader to focus on the core of the theory and techniques in the field. Further, detailed proofs make the work accessible to students at the graduate level.
Download or read book Maximal Subellipticity written by Brian Street and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-03 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Annales Academiae Scientiarum Fennicae written by and published by . This book was released on 2006 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Kolmogorov Operators and Their Applications written by Stéphane Menozzi and published by Springer Nature. This book was released on with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Function Spaces and Potential Theory written by David R. Adams and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: "..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
Download or read book Heat Kernels and Analysis on Manifolds Graphs and Metric Spaces written by Pascal Auscher and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.
Download or read book Issues in General and Specialized Mathematics Research 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Generalized Heisenberg Groups and Damek Ricci Harmonic Spaces written by Jürgen Berndt and published by Springer. This book was released on 2006-11-14 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Heisenberg groups, or H-type groups, introduced by A. Kaplan, and Damek-Ricci harmonic spaces are particularly nice Lie groups with a vast spectrum of properties and applications. These harmonic spaces are homogeneous Hadamard manifolds containing the H-type groups as horospheres. These notes contain a thorough study of their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators. Some problems are included and will hopefully stimulate further research on these spaces. The book is written for students and researchers, assuming only basic knowledge of Riemannian geometry, and it contains a brief survey of the background material needed to follow the entire treatment.
Download or read book Oblique Derivative Problems for Elliptic Equations in Conical Domains written by Mikhail Borsuk and published by Springer Nature. This book was released on 2023-05-31 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.
Download or read book Geometric Analysis of Quasilinear Inequalities on Complete Manifolds written by Bruno Bianchini and published by Springer Nature. This book was released on 2021-01-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Download or read book Stratified Lie Groups and Potential Theory for Their Sub Laplacians written by Andrea Bonfiglioli and published by Springer Science & Business Media. This book was released on 2007-08-24 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.
Download or read book Analytic Algebraic and Geometric Aspects of Differential Equations written by Galina Filipuk and published by Birkhäuser. This book was released on 2017-06-23 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
Download or read book Nonlinear Potential Theory on Metric Spaces written by Anders Björn and published by European Mathematical Society. This book was released on 2011 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Download or read book Introduction to Potential Theory written by Lester La Verne Helms and published by John Wiley & Sons. This book was released on 1969 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hardy Spaces on Homogeneous Groups MN 28 Volume 28 written by Gerald B. Folland and published by Princeton University Press. This book was released on 2020-12-08 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.
Download or read book Rectifiability written by Pertti Mattila and published by Cambridge University Press. This book was released on 2023-01-12 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside.
