Sobolev Maps To The Circle

Author : Haim Brezis,Petru Mironescu
Publisher : Springer Nature
Page : 552 pages
File Size : 46,7 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9781071615126

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Sobolev Maps to the Circle by Haim Brezis,Petru Mironescu Pdf

The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps. Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The “Complements and Open Problems” sections provide short introductions to various subsequent developments or related topics, and suggest newdirections of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena. Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.

Author : Henri Berestycki
Publisher : American Mathematical Soc.
Page : 495 pages
File Size : 52,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821841907

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Perspectives in Nonlinear Partial Differential Equations by Henri Berestycki Pdf

In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.

Author : George Dinca,Jean Mawhin
Publisher : Springer Nature
Page : 462 pages
File Size : 54,7 Mb
Release : 2021-05-11
Category : Mathematics
ISBN : 9783030632304

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Brouwer Degree by George Dinca,Jean Mawhin Pdf

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.

Author : Carmen Hurley &
Publisher : Scientific e-Resources
Page : 300 pages
File Size : 53,9 Mb
Release : 2018-11-11
Category : Electronic
ISBN : 9781839473401

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Wavelet by Carmen Hurley & Pdf

The idea of "e;ondelettes"e; or "e;wavelets"e; started from the investigation of time-frequency signal analysis, wave engendering, and examining hypothesis. One of the principle explanations behind the disclosure of wavelets and wavelet changes is that the Fourier change analysis does not contain the neighborhood data of signals. So the Fourier change can't be utilized for examining signals in a joint time and frequency area. In 1982, Jean MorIet, in a joint effort with a gathering of French designers, first presented the possibility of wavelets as a group of capacities built by utilizing interpretation and expansion of a solitary capacity, called the mother wavelet, for the analysis of nonstationary signals. Wavelet analysis is an energizing new technique for taking care of troublesome issues in science, material science, and building, with present day applications as various as wave spread, information pressure, picture preparing, design acknowledgment, PC illustrations, the location of air ship and submarines, and change in CAT filters and other restorative picture innovation. Wavelets permit complex data, for example, music, discourse, pictures, and examples to be deteriorated into basic structures, called the central building hinders, at various positions and scales and in this manner remade with high accuracy.

Author : Aleksander Strasburger
Publisher : Unknown
Page : 368 pages
File Size : 51,5 Mb
Release : 2002
Category : Finite groups
ISBN : UOM:39015056685145

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Geometry and Analysis on Finite- and Infinite-dimensional Lie Groups by Aleksander Strasburger Pdf

Author : Themistocles M. Rassias
Publisher : Springer
Page : 360 pages
File Size : 43,7 Mb
Release : 2018-06-18
Category : Mathematics
ISBN : 9783319898001

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Current Research in Nonlinear Analysis by Themistocles M. Rassias Pdf

Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians. Each contribution aims to broaden reader’s understanding of theories, methods, and techniques utilized to solve significant problems. Topics include: Sobolev Spaces Maximal monotone operators A theorem of Brezis-Nirenberg Operator-norm convergence of the Trotter product formula Elliptic operators with infinitely many variables Pseudo-and quasiconvexities for nonsmooth function Anisotropic surface measures Eulerian and Lagrangian variables Multiple periodic solutions of Lagrangian systems Porous medium equation Nondiscrete Lassonde-Revalski principle Graduate students and researchers in mathematics, physics, engineering, and economics will find this book a useful reference for new techniques and research areas. Haim Brezis and Louis Nirenberg’s fundamental research in nonlinear functional analysis and nonlinear partial differential equations along with their years of teaching and training students have had a notable impact in the field.

Author : Dimitrios Ntalampekos
Publisher : Springer Nature
Page : 186 pages
File Size : 51,7 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030508050

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Potential Theory on Sierpiński Carpets by Dimitrios Ntalampekos Pdf

This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpiński carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces. The first part focuses on the development of an innovative theory of harmonic functions that is suitable for Sierpiński carpets but differs from the classical approach of potential theory in metric spaces. The second part describes how this theory is utilized to prove a uniformization result for Sierpiński carpets. This book is intended for researchers in the fields of potential theory, quasiconformal geometry, geometric group theory, complex dynamics, geometric function theory and PDEs.

Author : Andreas Johann,Hans-Peter Kruse,Florian Rupp,Stephan Schmitz
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 42,8 Mb
Release : 2013-09-24
Category : Mathematics
ISBN : 9783034804516

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Recent Trends in Dynamical Systems by Andreas Johann,Hans-Peter Kruse,Florian Rupp,Stephan Schmitz Pdf

This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.

Author : Jürgen Erich Schmidt
Publisher : Walter de Gruyter
Page : 1148 pages
File Size : 50,5 Mb
Release : 2011-03-30
Category : Language Arts & Disciplines
ISBN : 9783110219166

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Language Mapping by Jürgen Erich Schmidt Pdf

The Handbook of Language Mapping aims to explore the core methodological and theoretical approaches of linguistic cartography. In both empirical and theoretical linguistics, the spatial variation of language is of increasing interest and the visualization of language in space is therefore also of growing significance. It is the precondition for correct data interpretation. But how does it work? What has to be considered when drawing a map? And how has the problem been tackled so far? This book provides answers to such questions by taking a closer look at the theoretical issues surrounding cartography and at the concrete practice of mapping. The fundamental issues raised are addressed particularly well, since linguistic geography is not only one of the domains with a lengthy tradition, it is also one of the most progressive fields in linguistics. At the same time, because of their visual primacy, linguistic maps directly confront the challenges of human perception and aesthetics. In this context, envisioning the fruits of language mapping is a fascinating and inspiring endeavor, not just for experts. With its accessible texts and wealth of full-color images, the handbook not only represents a comprehensive manual serving the interests of a variety of readers, it also fills a gap in the ongoing linguistic discourse.

Author : M. Jorge Cardoso,Tal Arbel,Enzo Ferrante,Xavier Pennec,Adrian V. Dalca,Sarah Parisot,Sarang Joshi,Nematollah K. Batmanghelich,Aristeidis Sotiras,Mads Nielsen,Mert R. Sabuncu,Tom Fletcher,Li Shen,Stanley Durrleman,Stefan Sommer
Publisher : Springer
Page : 262 pages
File Size : 46,5 Mb
Release : 2017-09-06
Category : Computers
ISBN : 9783319676753

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Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics by M. Jorge Cardoso,Tal Arbel,Enzo Ferrante,Xavier Pennec,Adrian V. Dalca,Sarah Parisot,Sarang Joshi,Nematollah K. Batmanghelich,Aristeidis Sotiras,Mads Nielsen,Mert R. Sabuncu,Tom Fletcher,Li Shen,Stanley Durrleman,Stefan Sommer Pdf

This book constitutes the refereed joint proceedings of the First International Workshop on Graphs in Biomedical Image Analysis, GRAIL 2017, the 6th International Workshop on Mathematical Foundations of Computational Anatomy, MFCA 2017, and the Third International Workshop on Imaging Genetics, MICGen 2017, held in conjunction with the 20th International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2017, in Québec City, QC, Canada, in September 2017. The 7 full papers presented at GRAIL 2017, the 10 full papers presented at MFCA 2017, and the 5 full papers presented at MICGen 2017 were carefully reviewed and selected. The GRAIL papers cover a wide range of graph based medical image analysis methods and applications, including probabilistic graphical models, neuroimaging using graph representations, machine learning for diagnosis prediction, and shape modeling. The MFCA papers deal with theoretical developments in non-linear image and surface registration in the context of computational anatomy. The MICGen papers cover topics in the field of medical genetics, computational biology and medical imaging.

Author : Albert Fathi,J.-C. Yoccoz
Publisher : Cambridge University Press
Page : 597 pages
File Size : 50,7 Mb
Release : 2006-02-02
Category : Mathematics
ISBN : 9780521860680

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Dynamical Systems by Albert Fathi,J.-C. Yoccoz Pdf

A collection of up-to-date research and classic papers reflecting the work of Michael Herman.

Author : Franco Giannessi,Antonino Maugeri
Publisher : Springer Science & Business Media
Page : 1163 pages
File Size : 53,7 Mb
Release : 2007-03-06
Category : Mathematics
ISBN : 9780387242767

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Variational Analysis and Applications by Franco Giannessi,Antonino Maugeri Pdf

This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.

Author : Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui
Publisher : Birkhäuser
Page : 158 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879682

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Variational Problems in Riemannian Geometry by Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui Pdf

This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.

Author : Kurusch Ebrahimi-Fard
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 48,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853290

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Combinatorics and Physics by Kurusch Ebrahimi-Fard Pdf

This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.

Author : Jerzy Jezierski,Waclaw Marzantowicz
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 51,5 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9781402039317

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Homotopy Methods in Topological Fixed and Periodic Points Theory by Jerzy Jezierski,Waclaw Marzantowicz Pdf

The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.