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Direct Methods In The Theory Of Elliptic Equations
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Book Synopsis Direct Methods in the Theory of Elliptic Equations by : Jindrich Necas
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.
Book Synopsis Direct Methods in the Theory of Elliptic Equations by : Jindrich Necas
Download or read book Direct Methods in the Theory of Elliptic Equations written by Jindrich Necas and published by Springer. This book was released on 2011-10-09 with total page 372 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.
Book Synopsis Direct Methods in the Calculus of Variations by : Enrico Giusti
Download or read book Direct Methods in the Calculus of Variations written by Enrico Giusti and published by World Scientific. This book was released on 2003 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.
Book Synopsis Elliptic Differential Equations by : W. Hackbusch
Download or read book Elliptic Differential Equations written by W. Hackbusch and published by Springer Science & Business Media. This book was released on 1992 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR
Book Synopsis Elliptic Marching Methods and Domain Decomposition by : Patrick J. Roache
Download or read book Elliptic Marching Methods and Domain Decomposition written by Patrick J. Roache and published by CRC Press. This book was released on 1995-06-29 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial differential equations. Elliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathematics, and the physical sciences.
Book Synopsis Constructive Methods for Elliptic Equations by : R.P. Gilbert
Download or read book Constructive Methods for Elliptic Equations written by R.P. Gilbert and published by Springer. This book was released on 2006-11-15 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily these lectures are a report on recent work by the Indiana University group working on Function theoretic methods as applied to the theory of partial differential equations.
Book Synopsis Elliptic Differential Equations by : Wolfgang Hackbusch
Download or read book Elliptic Differential Equations written by Wolfgang Hackbusch and published by . This book was released on 2010-11-20 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Numerical Solution of Elliptic Equations by : Garrett Birkhoff
Download or read book The Numerical Solution of Elliptic Equations written by Garrett Birkhoff and published by SIAM. This book was released on 1971-01-01 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.
Book Synopsis Constructive Methods for Elliptic Equations by : R. P. Gilbert
Download or read book Constructive Methods for Elliptic Equations written by R. P. Gilbert and published by . This book was released on 2014-01-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Elliptic Partial Differential Equations by : Hervé Le Dret
Download or read book Nonlinear Elliptic Partial Differential Equations written by Hervé Le Dret and published by Springer. This book was released on 2018-05-25 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.
Book Synopsis Partial Differential Equations 2 by : Friedrich Sauvigny
Download or read book Partial Differential Equations 2 written by Friedrich Sauvigny and published by Springer Science & Business Media. This book was released on 2006-10-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.
Book Synopsis Elliptic Equations: An Introductory Course by : Michel Chipot
Download or read book Elliptic Equations: An Introductory Course written by Michel Chipot and published by Springer Nature. This book was released on with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs by : Mariano Giaquinta
Download or read book An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and L^p-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the L^p theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.
Book Synopsis use of fast direct methods for the efficient num erical solution of nonseparable elliptic equations by : gene h golub
Download or read book use of fast direct methods for the efficient num erical solution of nonseparable elliptic equations written by gene h golub and published by . This book was released on 1972 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations by : Stanford University. Computer Science Department
Download or read book Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations written by Stanford University. Computer Science Department and published by . This book was released on 1972 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Partial Differential Equations by : Qing Han
Download or read book Elliptic Partial Differential Equations written by Qing Han and published by American Mathematical Soc.. This book was released on 2011 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
Book Synopsis Introduction to the Theory of Nonlinear Elliptic Equations by : Jindric Necas
Download or read book Introduction to the Theory of Nonlinear Elliptic Equations written by Jindric Necas and published by . This book was released on 1986-12-29 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the study of boundary value problems for nonlinear, second order, elliptic partial differential equations. A short introduction to Sobolev and Morrey-Campanato spaces and to methods of approximation is included.
