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Author : James E. Calvert
Publisher :
ISBN 13 :
Total Pages : 98 pages
Book Rating : 4.:/5 (29 download)
Download or read book Integral Inequalities with Applications to the Dirichlet Problem written by James E. Calvert and published by . This book was released on 1966 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dragoslav S. Mitrinovic
Publisher : Springer Science & Business Media
ISBN 13 : 9401135622
Total Pages : 602 pages
Book Rating : 4.4/5 (11 download)
Download or read book Inequalities Involving Functions and Their Integrals and Derivatives written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Dorin Andrica
Publisher : Springer Nature
ISBN 13 : 3030274071
Total Pages : 848 pages
Book Rating : 4.0/5 (32 download)
Download or read book Differential and Integral Inequalities written by Dorin Andrica and published by Springer Nature. This book was released on 2019-11-14 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.
Author : B. Opic
Publisher :
ISBN 13 : 9780608035987
Total Pages : 351 pages
Book Rating : 4.0/5 (359 download)
Download or read book Hardy-Type Inequalities written by B. Opic and published by . This book was released on 1990-01-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ravi P. Agarwal
Publisher : Springer Nature
ISBN 13 : 3030690296
Total Pages : 607 pages
Book Rating : 4.0/5 (36 download)
Download or read book Lyapunov Inequalities and Applications written by Ravi P. Agarwal and published by Springer Nature. This book was released on 2021-04-12 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.
Author : Siegfried Carl
Publisher : Springer Science & Business Media
ISBN 13 : 038746252X
Total Pages : 404 pages
Book Rating : 4.3/5 (874 download)
Download or read book Nonsmooth Variational Problems and Their Inequalities written by Siegfried Carl and published by Springer Science & Business Media. This book was released on 2007-06-07 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.
Author : Vladimir Maz'ya
Publisher : Springer
ISBN 13 : 3662099225
Total Pages : 506 pages
Book Rating : 4.6/5 (62 download)
Download or read book Sobolev Spaces written by Vladimir Maz'ya and published by Springer. This book was released on 2013-12-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q
Author : R.P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9401730040
Total Pages : 412 pages
Book Rating : 4.4/5 (17 download)
Download or read book Singular Differential and Integral Equations with Applications written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last century many problems which arose in the science, engineer ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This mono graph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest. In Chapter 1 we study differential equations which are singular in the independent variable. We begin with some standard notation in Section 1. 2 and introduce LP-Caratheodory functions. Some fixed point theorems, the Arzela- Ascoli theorem and Banach's theorem are also stated here.
Author : Christian G Simader
Publisher : CRC Press
ISBN 13 : 9780582209534
Total Pages : 308 pages
Book Rating : 4.2/5 (95 download)
Download or read book The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains written by Christian G Simader and published by CRC Press. This book was released on 1996-11-07 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dirichlet Problem -?u=ƒ in G, u|?G=0 for the Laplacian in a domain GÌRn with boundary ?G is one of the basic problems in the theory of partial differential equations and it plays a fundamental role in mathematical physics and engineering.
Author :
Publisher :
ISBN 13 :
Total Pages : 1278 pages
Book Rating : 4.:/5 (31 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1984 with total page 1278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alois Kufner
Publisher : World Scientific
ISBN 13 : 9789812381958
Total Pages : 380 pages
Book Rating : 4.3/5 (819 download)
Download or read book Weighted Inequalities of Hardy Type written by Alois Kufner and published by World Scientific. This book was released on 2003 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 fields 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. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.
Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821868896
Total Pages : 545 pages
Book Rating : 4.8/5 (218 download)
Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Author : Melvyn S. Berger
Publisher : Academic Press
ISBN 13 : 0080570445
Total Pages : 439 pages
Book Rating : 4.0/5 (85 download)
Download or read book Nonlinearity and Functional Analysis written by Melvyn S. Berger and published by Academic Press. This book was released on 1977-10-27 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinearity and Functional Analysis is a collection of lectures that aim to present a systematic description of fundamental nonlinear results and their applicability to a variety of concrete problems taken from various fields of mathematical analysis. For decades, great mathematical interest has focused on problems associated with linear operators and the extension of the well-known results of linear algebra to an infinite-dimensional context. This interest has been crowned with deep insights, and the substantial theory that has been developed has had a profound influence throughout the mathematical sciences. This volume comprises six chapters and begins by presenting some background material, such as differential-geometric sources, sources in mathematical physics, and sources from the calculus of variations, before delving into the subject of nonlinear operators. The following chapters then discuss local analysis of a single mapping and parameter dependent perturbation phenomena before going into analysis in the large. The final chapters conclude the collection with a discussion of global theories for general nonlinear operators and critical point theory for gradient mappings. This book will be of interest to practitioners in the fields of mathematics and physics, and to those with interest in conventional linear functional analysis and ordinary and partial differential equations.
Author : Alan Jeffrey
Publisher : CRC Press
ISBN 13 : 158488553X
Total Pages : 594 pages
Book Rating : 4.5/5 (848 download)
Download or read book Complex Analysis and Applications, Second Edition written by Alan Jeffrey and published by CRC Press. This book was released on 2005-11-10 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems. A discussion of complex analysis now forms the first three chapters of the book, with a description of conformal mapping and its application to boundary value problems for the two-dimensional Laplace equation forming the final two chapters. This new structure enables students to study theory and applications separately, as needed. In order to maintain brevity and clarity, the text limits the application of complex analysis to two-dimensional boundary value problems related to temperature distribution, fluid flow, and electrostatics. In each case, in order to show the relevance of complex analysis, each application is preceded by mathematical background that demonstrates how a real valued potential function and its related complex potential can be derived from the mathematics that describes the physical situation.
Author : Jindrich Necas
Publisher : Springer Science & Business Media
ISBN 13 : 364210455X
Total Pages : 384 pages
Book Rating : 4.6/5 (421 download)
Download or read book Direct Methods in the Theory of Elliptic Equations written by Jindrich Necas and published by Springer Science & Business Media. This book was released on 2011-10-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library. The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame’s system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lame system and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications.
Author : Alexei Alexandrov
Publisher : American Mathematical Soc.
ISBN 13 : 0821890786
Total Pages : 275 pages
Book Rating : 4.8/5 (218 download)
Download or read book Linear and Complex Analysis written by Alexei Alexandrov and published by American Mathematical Soc.. This book was released on with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J N Flavin
Publisher : CRC Press
ISBN 13 : 1000099350
Total Pages : 389 pages
Book Rating : 4.0/5 ( download)
Download or read book Qualitative Estimates For Partial Differential Equations written by J N Flavin and published by CRC Press. This book was released on 2020-12-17 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Qualitative Estimates For Partial Differential Equations: An Introduction describes an approach to the use of partial differential equations (PDEs) arising in the modelling of physical phenomena. It treats a wide range of differential inequality techniques applicable to problems arising in engineering and the natural sciences, including fluid and solid mechanics, physics, dynamics, biology, and chemistry. The book begins with an elementary discussion of the fundamental principles of differential inequality techniques for PDEs arising in the solution of physical problems, and then shows how these are used in research. Qualitative Estimates For Partial Differential Equations: An Introduction is an ideal book for students, professors, lecturers, and researchers who need a comprehensive introduction to qualitative methods for PDEs arising in engineering and the natural sciences.
