Differentiability In Banach Spaces Differential Forms And Applications

Author : Celso Melchiades Doria
Publisher : Springer Nature
Page : 362 pages
File Size : 41,6 Mb
Release : 2021-07-19
Category : Mathematics
ISBN : 9783030778347

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Differentiability in Banach Spaces, Differential Forms and Applications by Celso Melchiades Doria Pdf

This book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.

Author : R. Nottrot
Publisher : Lecture Notes in Mathematics
Page : 140 pages
File Size : 51,8 Mb
Release : 1982-12
Category : Mathematics
ISBN : UOM:39015049384137

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Optimal Processes on Manifolds by R. Nottrot Pdf

Author : Serge Lang
Publisher : Unknown
Page : 148 pages
File Size : 43,6 Mb
Release : 1962
Category : Differentiable manifolds
ISBN : UOM:39015015608600

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Introduction to Differentiable Manifolds by Serge Lang Pdf

Author : Joram Lindenstrauss,David Preiss,Jaroslav Tišer
Publisher : Princeton University Press
Page : 440 pages
File Size : 55,7 Mb
Release : 2012-02-26
Category : Mathematics
ISBN : 9780691153568

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Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces by Joram Lindenstrauss,David Preiss,Jaroslav Tišer Pdf

This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics.

Author : Schaefer, Uwe
Publisher : KIT Scientific Publishing
Page : 150 pages
File Size : 52,9 Mb
Release : 2014-12-03
Category : Mathematics
ISBN : 9783731502609

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From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications by Schaefer, Uwe Pdf

Based on Sperner's lemma the fixed point theorem of Brouwer is proved. Rather than presenting also other beautiful proofs of Brouwer's fixed point theorem, many nice applications are given in some detail. Also Schauder's fixed point theorem is presented which can be viewed as a natural generalization of Brouwer's fixed point theorem to an infinite-dimensional setting. Finally, Tarski's fixed point theorem is applied to differential equations in Banach spaces.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241829

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Differential and Riemannian Manifolds by Serge Lang Pdf

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

Author : S. M. Nikol'skii
Publisher : American Mathematical Soc.
Page : 348 pages
File Size : 53,7 Mb
Release : 1982-12-31
Category : Mathematics
ISBN : 0821830473

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Theory and Applications of Differentiable Functions of Several Variables by S. M. Nikol'skii Pdf

Author : L. Veselý,L. Zajíc̆ek
Publisher : Unknown
Page : 60 pages
File Size : 54,6 Mb
Release : 1989
Category : Banach spaces
ISBN : UCR:31210012616486

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Delta-convex Mappings Between Banach Spaces and Applications by L. Veselý,L. Zajíc̆ek Pdf

Author : Robert R. Phelps
Publisher : Springer
Page : 125 pages
File Size : 47,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783662215692

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Convex Functions, Monotone Operators and Differentiability by Robert R. Phelps Pdf

These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.

Author : Serge Lang
Publisher : Unknown
Page : 564 pages
File Size : 45,5 Mb
Release : 1998-12-01
Category : Electronic
ISBN : 1461205425

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Fundamentals of Differential Geometry by Serge Lang Pdf

Author : Alfred Frölicher,Andreas Kriegl
Publisher : Unknown
Page : 272 pages
File Size : 43,9 Mb
Release : 1988-08-18
Category : Mathematics
ISBN : UCAL:B5008829

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Linear Spaces and Differentiation Theory by Alfred Frölicher,Andreas Kriegl Pdf

This book presents a new basis for differential calculus. Classical differentiation in linear spaces of arbitrary dimension uses Banach spaces--but most function spaces are not Banach spaces. Any attempts to develop a theory of differentiation covering non-normable linear spaces have always involved arbitrary conditions. This book bases the theory of differentiability of linear spaces on the fundamental idea of reducing the differentiability of general maps to that of functions on the real numbers. And the property ``continuously differentiable'' is replaced by that of ``Lipschitz differentiable.'' The result is a more natural theory, of conceptual simplicity that leads to the the same categories of linear spaces, but in a more general setting.

Author : Angelo Favini,Atsushi Yagi
Publisher : CRC Press
Page : 336 pages
File Size : 52,8 Mb
Release : 1998-09-10
Category : Mathematics
ISBN : 9781482276022

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Degenerate Differential Equations in Banach Spaces by Angelo Favini,Atsushi Yagi Pdf

This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the an

Author : Ravi P. Agarwal,Shusen Ding,Craig Nolder
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 49,7 Mb
Release : 2009-09-19
Category : Mathematics
ISBN : 9780387684178

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Inequalities for Differential Forms by Ravi P. Agarwal,Shusen Ding,Craig Nolder Pdf

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Author : Serge Lang
Publisher : Unknown
Page : 244 pages
File Size : 42,6 Mb
Release : 1985
Category : Differentiable manifolds
ISBN : STANFORD:36105032860814

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Differential Manifolds by Serge Lang Pdf

Author : Kondagunta Sundaresan,Srinivasa Swaminathan
Publisher : Springer
Page : 120 pages
File Size : 44,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540394150

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Geometry and Nonlinear Analysis in Banach Spaces by Kondagunta Sundaresan,Srinivasa Swaminathan Pdf