Inequalities For Differential Forms

Author : Ravi P. Agarwal,Shusen Ding,Craig Nolder
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 48,5 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 : V. Lakshmikantham,S. Leela
Publisher : Academic Press
Page : 389 pages
File Size : 40,6 Mb
Release : 1969
Category : Computers
ISBN : 9780080955636

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Differential and Integral Inequalities: Theory and Applications by V. Lakshmikantham,S. Leela Pdf

This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applications of differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.

Author : Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland
Publisher : Birkhäuser
Page : 313 pages
File Size : 40,7 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9783319470795

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Recent Trends in Operator Theory and Partial Differential Equations by Vladimir Maz'ya,David Natroshvili,Eugene Shargorodsky,Wolfgang L. Wendland Pdf

This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.

Author : Alois Kufner,Lars-Erik Persson,Natasha Samko
Publisher : World Scientific Publishing Company
Page : 480 pages
File Size : 41,5 Mb
Release : 2017-06-16
Category : Electronic
ISBN : 9789813140660

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Weighted Inequalities of Hardy Type by Alois Kufner,Lars-Erik Persson,Natasha Samko Pdf

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy–Steklov operators, and some basic results about Hardy-type inequalities and their limit (Carleman–Knopp type) inequalities. It also describes some rather new areas such as higher order and fractional order Hardy-type inequalities and integral inequalities on the cone of monotone functions, together with some applications and open problems. In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions. Request Inspection Copy

Author : Anonim
Publisher : Elsevier
Page : 623 pages
File Size : 40,7 Mb
Release : 1997-11-12
Category : Mathematics
ISBN : 9780080534640

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Inequalities for Differential and Integral Equations by Anonim Pdf

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course. Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books Provides a valuable reference to engineers and graduate students

Author : Lakshmikantham
Publisher : Academic Press
Page : 316 pages
File Size : 42,7 Mb
Release : 1969
Category : Computers
ISBN : 9780080955643

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Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations by Lakshmikantham Pdf

Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations

Author : George A. Anastassiou,John Michael Rassias
Publisher : Springer Nature
Page : 746 pages
File Size : 52,5 Mb
Release : 2019-11-23
Category : Mathematics
ISBN : 9783030289508

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Frontiers in Functional Equations and Analytic Inequalities by George A. Anastassiou,John Michael Rassias Pdf

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

Author : Guillemin Victor,Haine Peter
Publisher : World Scientific
Page : 272 pages
File Size : 42,5 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9789813272798

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Differential Forms by Guillemin Victor,Haine Peter Pdf

There already exist a number of excellent graduate textbooks on the theory of differential forms as well as a handful of very good undergraduate textbooks on multivariable calculus in which this subject is briefly touched upon but not elaborated on enough.The goal of this textbook is to be readable and usable for undergraduates. It is entirely devoted to the subject of differential forms and explores a lot of its important ramifications.In particular, our book provides a detailed and lucid account of a fundamental result in the theory of differential forms which is, as a rule, not touched upon in undergraduate texts: the isomorphism between the Čech cohomology groups of a differential manifold and its de Rham cohomology groups.

Author : Gabriel-Eduard Vîlcu
Publisher : MDPI
Page : 208 pages
File Size : 50,8 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9783036502984

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Inequalities in Geometry and Applications by Gabriel-Eduard Vîlcu Pdf

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Author : Michael Farber
Publisher : American Mathematical Soc.
Page : 246 pages
File Size : 46,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835319

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Topology of Closed One-forms by Michael Farber Pdf

This monograph is an introduction to the fascinating field of the topology, geometry and dynamics of closed one-forms. The subject was initiated by S. P. Novikov in 1981 as a study of Morse type zeros of closed one-forms. The first two chapters of the book, written in textbook style, give a detailed exposition of Novikov theory, which plays a fundamental role in geometry and topology. Subsequent chapters of the book present a variety of topics where closed one-forms play a central role. The most significant results are the following: the solution of the problem of exactness of the Novikov inequalities for manifolds with the infinite cyclic fundamental group; the solution of a problem raised by E. Calabi about intrinsically harmonic closed one-forms and their Morse numbers; and, the construction of a universal chain complex which bridges the topology of the underlying manifold with information about zeros of closed one-forms.This complex implies many interesting inequalities including Bott-type inequalities, equivariant inequalities, and inequalities involving von Neumann Betti numbers. The construction of a novel Lusternik-Schnirelman-type theory for dynamical systems. Closed one-forms appear in dynamics through the concept of a Lyapunov one-form of a flow. As is shown in the book, homotopy theory may be used to predict the existence of homoclinic orbits and homoclinic cycles in dynamical systems ('focusing effect').

Author : E.W. Stredulinsky
Publisher : Springer
Page : 149 pages
File Size : 50,8 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540389286

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Weighted Inequalities and Degenerate Elliptic Partial Differential Equations by E.W. Stredulinsky Pdf

Author : Elliott H. Lieb
Publisher : Springer Science & Business Media
Page : 711 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642559259

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Inequalities by Elliott H. Lieb Pdf

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Author : Isaac Chavel
Publisher : Cambridge University Press
Page : 292 pages
File Size : 54,9 Mb
Release : 2001-07-23
Category : Mathematics
ISBN : 0521802679

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Isoperimetric Inequalities by Isaac Chavel Pdf

This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.

Author : Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink
Publisher : Springer Science & Business Media
Page : 602 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401135627

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Inequalities Involving Functions and Their Integrals and Derivatives by Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink Pdf

One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 1969
Category : Electronic
ISBN : OCLC:1137389831

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Differential and Integral Inequalities: Theory and Applications. Volume I: Ordinary Differential Equations by Anonim Pdf