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Author : Grigoriĭ Ilʹich Eskin
Publisher :
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.3/5 (91 download)
Download or read book Boundary Value Problems for Elliptic Pseudodifferential Equations written by Grigoriĭ Ilʹich Eskin and published by . This book was released on 1981 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M.S. Agranovich
Publisher : Springer Science & Business Media
ISBN 13 : 3662067218
Total Pages : 287 pages
Book Rating : 4.6/5 (62 download)
Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.
Author : J. T. Wloka
Publisher : Cambridge University Press
ISBN 13 : 0521430119
Total Pages : 659 pages
Book Rating : 4.5/5 (214 download)
Download or read book Boundary Value Problems for Elliptic Systems written by J. T. Wloka and published by Cambridge University Press. This book was released on 1995-07-28 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators, and matrix analysis.
Author : M.S. Agranovich
Publisher : Springer
ISBN 13 : 9783662067222
Total Pages : 284 pages
Book Rating : 4.0/5 (672 download)
Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer. This book was released on 2014-03-12 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.
Author : George Chkadua
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)
Download or read book Pseudodifferential Operators and Boundary Value Problems for Elliptic Equations and Systems written by George Chkadua and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate asymptotics of fundamental solutions of the hypoelliptic differential equation where the corresponding characteristic polynomial has real multiple zeros. Based on the asymptotic expansion of a fundamental solution we introduce asymptotic classes of distributions and prove existence and uniqueness of solutions in those classes. Our results imply in particular, a new uniqueness theorem for the classical Helmhotz equation. We study a model of fluid-solid acoustic interaction when a piezo-ceramic elastic body ( n+) is embedded in an unbounded fluid domain ( n-). In the bounded domain n+, we have 4 x 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain n- we have a scalar Helmholtz equation describing acoustic wave propagation. We consider the Dirichlet (Dw), Neumann (Nw) and mixed type (Mw) interaction problems. The physical kinematic and dynamic relations are described mathematically by appropriate boundary and transmission conditions. With the help of the boundary integral equations method and theory of pseudodifferential equations based on the Wiener-Hopf factorization method, we prove uniqueness and existence theorems in Sobolev-Slobodetskii spaces. We derive asymptotic expansions of solutions of the mixed type interaction problem near the line where different boundary conditions meet, and on the basis of our asymptotic analysis, we establish optimal Holder smoothness results for solutions. We also consider three-dimensional Riquier-type and classical mixed boundary value problems for the polymetaharmonic equation We prove existence and uniqueness theorems in Sobolev-Slobodetskii spaces, analyse asymptotic properties of solutions and establish optimal H6lder smoothness results for solutions.
Author : M.S. Agranovich
Publisher : Springer
ISBN 13 : 9783540570448
Total Pages : 300 pages
Book Rating : 4.5/5 (74 download)
Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer. This book was released on 1996-12-16 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.
Author : Xiaochun Liu
Publisher : Birkhäuser
ISBN 13 : 3319701142
Total Pages : 410 pages
Book Rating : 4.3/5 (197 download)
Download or read book Boundary Value Problems with Global Projection Conditions written by Xiaochun Liu and published by Birkhäuser. This book was released on 2018-10-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel’s calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.
Author : Vladimir Kozlov
Publisher : American Mathematical Soc.
ISBN 13 : 0821807544
Total Pages : 426 pages
Book Rating : 4.8/5 (218 download)
Download or read book Elliptic Boundary Value Problems in Domains with Point Singularities written by Vladimir Kozlov and published by American Mathematical Soc.. This book was released on 1997 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR
Author : V. Vasil'ev
Publisher : Springer Science & Business Media
ISBN 13 : 9401594481
Total Pages : 184 pages
Book Rating : 4.4/5 (15 download)
Download or read book Wave Factorization of Elliptic Symbols: Theory and Applications written by V. Vasil'ev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: To summarize briefly, this book is devoted to an exposition of the foundations of pseudo differential equations theory in non-smooth domains. The elements of such a theory already exist in the literature and can be found in such papers and monographs as [90,95,96,109,115,131,132,134,135,136,146, 163,165,169,170,182,184,214-218]. In this book, we will employ a theory that is based on quite different principles than those used previously. However, precisely one of the standard principles is left without change, the "freezing of coefficients" principle. The first main difference in our exposition begins at the point when the "model problem" appears. Such a model problem for differential equations and differential boundary conditions was first studied in a fundamental paper of V. A. Kondrat'ev [134]. Here also the second main difference appears, in that we consider an already given boundary value problem. In some transformations this boundary value problem was reduced to a boundary value problem with a parameter . -\ in a domain with smooth boundary, followed by application of the earlier results of M. S. Agranovich and M. I. Vishik. In this context some operator-function R('-\) appears, and its poles prevent invertibility; iffor differential operators the function is a polynomial on A, then for pseudo differential operators this dependence on . -\ cannot be defined. Ongoing investigations of different model problems are being carried out with approximately this plan, both for differential and pseudodifferential boundary value problems.
Author : Bernhelm Booß-Bavnbek
Publisher : Springer Science & Business Media
ISBN 13 : 1461203376
Total Pages : 322 pages
Book Rating : 4.4/5 (612 download)
Download or read book Elliptic Boundary Problems for Dirac Operators written by Bernhelm Booß-Bavnbek and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic boundary problems have enjoyed interest recently, espe cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.
Author : Gerd Grubb
Publisher : Springer Science & Business Media
ISBN 13 : 9780817637385
Total Pages : 544 pages
Book Rating : 4.6/5 (373 download)
Download or read book Functional Calculus of Pseudodifferential Boundary Problems written by Gerd Grubb and published by Springer Science & Business Media. This book was released on 1996-01-26 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel (brought completely up to date in this edition) and in version containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, index theory, fractional powers, spectral theory and singular perturbation theory. Thus the book’s improved proofs and modern points of view will be useful to research mathematicians and to graduate students studying partial differential equations and pseudodifferential operators.
Author : A. Avantaggiati
Publisher : Springer Science & Business Media
ISBN 13 : 3642110924
Total Pages : 238 pages
Book Rating : 4.6/5 (421 download)
Download or read book Pseudodifferential Operators with Applications written by A. Avantaggiati and published by Springer Science & Business Media. This book was released on 2011-06-07 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: A. Dynin: Pseudo-differential operators on Heisenberg groups.- A. Dynin: An index formula for elliptic boundary problems.- G.I. Eskin: General mixed boundary problems for elliptic differential equations.- B. Helffer: Hypoellipticité pour des opérateurs différentiels sur des groupes de Lie nilpotents.- J.J. Kohn: Lectures on degenerate elliptic problems.- K. Taira: Conditions nécessaires et suffisantes pour l’existence et l’unicité des solutions du problème de la dérivée oblique.- F. Treves: Boundary value problems for elliptic equations.
Author : Guo Chun Wen
Publisher : Chapman & Hall/CRC
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.F/5 ( download)
Download or read book Boundary Value Problems for Elliptic Equations and Systems written by Guo Chun Wen and published by Chapman & Hall/CRC. This book was released on 1990 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph mainly deals with several boundary value problems for linear and nonlinear elliptic equations and systems by using function theoretic methods. The established theory is systematic, the considered equations and systems, boundary conditions and domains are rather general. Various methods are used. As an application, the existence of nonlinear quasiconformal mappings onto canonical domains is proved.
Author : Shmuel Agmon
Publisher : American Mathematical Soc.
ISBN 13 : 0821849107
Total Pages : 225 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lectures on Elliptic Boundary Value Problems written by Shmuel Agmon and published by American Mathematical Soc.. This book was released on 2010-02-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is a new edition of a book originally published in 1965, presents an introduction to the theory of higher-order elliptic boundary value problems. The book contains a detailed study of basic problems of the theory, such as the problem of existence and regularity of solutions of higher-order elliptic boundary value problems. It also contains a study of spectral properties of operators associated with elliptic boundary value problems. Weyl's law on the asymptotic distribution of eigenvalues is studied in great generality.
Author : Olga Lepsky
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (129 download)
Download or read book Investigation of the Boundary Integral Equations of Elliptic Boundary Value Problems with the Help of Pseudo-differential Operators written by Olga Lepsky and published by . This book was released on 1996 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gerd Grubb
Publisher : Springer Science & Business Media
ISBN 13 : 146120769X
Total Pages : 536 pages
Book Rating : 4.4/5 (612 download)
Download or read book Functional Calculus of Pseudodifferential Boundary Problems written by Gerd Grubb and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel (brought completely up to date in this edition) and in version containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, index theory, fractional powers, spectral theory and singular perturbation theory. Thus the book’s improved proofs and modern points of view will be useful to research mathematicians and to graduate students studying partial differential equations and pseudodifferential operators.
Author : Michael Eugene Taylor
Publisher : Princeton University Press
ISBN 13 : 1400886104
Total Pages : 464 pages
Book Rating : 4.4/5 (8 download)
Download or read book Pseudodifferential Operators (PMS-34) written by Michael Eugene Taylor and published by Princeton University Press. This book was released on 2017-03-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here Michael Taylor develops pseudodifferential operators as a tool for treating problems in linear partial differential equations, including existence, uniqueness, and estimates of smoothness, as well as other qualitative properties. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
