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Author : Eugenio Massa
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.3/5 (91 download)
Download or read book On the Fučík Spectrum for Elliptic Systems written by Eugenio Massa and published by . This book was released on 2005 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pekka Neittaanmaki
Publisher : Springer Science & Business Media
ISBN 13 : 0387272364
Total Pages : 514 pages
Book Rating : 4.3/5 (872 download)
Download or read book Optimization of Elliptic Systems written by Pekka Neittaanmaki and published by Springer Science & Business Media. This book was released on 2007-01-04 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.
Author : Wolfgang L. Wendland
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.:/5 (44 download)
Download or read book Elliptic Systems in the Plane written by Wolfgang L. Wendland and published by Pitman Publishing. This book was released on 1979 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Nicholas D. Alikakos
Publisher : Springer
ISBN 13 : 3319905724
Total Pages : 343 pages
Book Rating : 4.3/5 (199 download)
Download or read book Elliptic Systems of Phase Transition Type written by Nicholas D. Alikakos and published by Springer. This book was released on 2019-01-21 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes – non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was settled in a series of papers: Ghoussoub and Gui (2d), Ambrosio and Cabré (3d), Savin (up to 8d), and del Pino, Kowalczyk and Wei (counterexample for 9d and above). This book extends, in various ways, the Caffarelli-Córdoba density estimates that played a major role in Savin's proof. It also introduces an alternative method for obtaining pointwise estimates. Key features and topics of this self-contained, systematic exposition include: • Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions. • Preliminary material beginning with the stress-energy tensor, via which monotonicity formulas, and Hamiltonian and Pohozaev identities are developed, including a self-contained exposition of the existence of standing and traveling waves. • Tools that allow the derivation of general properties of minimizers, without any assumptions of symmetry, such as a maximum principle or density and pointwise estimates. • Application of the general tools to equivariant solutions rendering exponential estimates, rigidity theorems and stratification results. This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations – ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or the applied mathematics of materials science.
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)
Download or read book The Essential Spectrum of Elliptic Systems of Mixed Order written by and published by . This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michel Chipot
Publisher : Springer Nature
ISBN 13 : 3031541235
Total Pages : 393 pages
Book Rating : 4.0/5 (315 download)
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:
Author : Yazhe Chen
Publisher : Amer Mathematical Society
ISBN 13 : 9780821809709
Total Pages : 246 pages
Book Rating : 4.8/5 (97 download)
Download or read book Second Order Elliptic Equations and Elliptic Systems written by Yazhe Chen and published by Amer Mathematical Society. This book was released on 1998-01-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book presents a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations are completely introduced. In the second part, the existence and regularity theory of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students.
Author : Friedmar Schulz
Publisher : Springer
ISBN 13 :
Total Pages : 752 pages
Book Rating : 4.:/5 (321 download)
Download or read book Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions written by Friedmar Schulz and published by Springer. This book was released on 1990 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Author : J. P. Gossez
Publisher : American Mathematical Soc.
ISBN 13 : 0821849077
Total Pages : 278 pages
Book Rating : 4.8/5 (218 download)
Download or read book Nonlinear Elliptic Partial Differential Equations written by J. P. Gossez and published by American Mathematical Soc.. This book was released on 2011 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.
Author : Ya-Zhe Chen
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889619
Total Pages : 268 pages
Book Rating : 4.8/5 (896 download)
Download or read book Second Order Elliptic Equations and Elliptic Systems written by Ya-Zhe Chen and published by American Mathematical Soc.. This book was released on with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.
Author : Eugenio Massa
Publisher :
ISBN 13 :
Total Pages : 137 pages
Book Rating : 4.:/5 (14 download)
Download or read book On the Fučík Spectrum and Superlinear Elliptic Equations written by Eugenio Massa and published by . This book was released on 2003 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : G. Geymonat
Publisher :
ISBN 13 :
Total Pages : 53 pages
Book Rating : 4.:/5 (897 download)
Download or read book The Essential Spectrum of Elliptic Systems of Mixed Order written by G. Geymonat and published by . This book was released on 1976 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gershon Kresin
Publisher : American Mathematical Soc.
ISBN 13 : 0821889818
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)
Download or read book Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems written by Gershon Kresin and published by American Mathematical Soc.. This book was released on 2012-08-15 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
Author : Friedmar Schulz
Publisher :
ISBN 13 : 9783662188026
Total Pages : 148 pages
Book Rating : 4.1/5 (88 download)
Download or read book Regularity Theory for Quasilinear Elliptic Systems and Monge - Ampere Equations in Two Dimensions written by Friedmar Schulz and published by . This book was released on 2014-01-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C. Wayne Mastin
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (317 download)
Download or read book Elliptic Systems and Numerical Transformations written by C. Wayne Mastin and published by . This book was released on 1976 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jindrich Necas
Publisher : Springer
ISBN 13 : 9783642104565
Total Pages : 372 pages
Book Rating : 4.1/5 (45 download)
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.
