Pseudodifferential Operators And Boundary Value Problems For Elliptic Equations And Systems

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Boundary Value Problems for Elliptic Systems

Author : J. T. Wloka
Publisher : Cambridge University Press
ISBN 13 : 0521430119
Total Pages : 659 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Boundary Value Problems for Elliptic Systems by : J. T. Wloka

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.

Pseudodifferential Operators and Boundary Value Problems for Elliptic Equations and Systems

Author : George Chkadua
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)

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Book Synopsis Pseudodifferential Operators and Boundary Value Problems for Elliptic Equations and Systems by : George Chkadua

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.

Partial Differential Equations IX

Author : M.S. Agranovich
Publisher : Springer Science & Business Media
ISBN 13 : 3662067218
Total Pages : 287 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Partial Differential Equations IX by : M.S. Agranovich

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.

Pseudodifferential Operators with Applications

Author : A. Avantaggiati
Publisher : Springer Science & Business Media
ISBN 13 : 3642110924
Total Pages : 238 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Pseudodifferential Operators with Applications by : A. Avantaggiati

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.

Pseudo-differential Operators

Author : Louis Nirenberg
Publisher : Springer Science & Business Media
ISBN 13 : 3642110746
Total Pages : 363 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Pseudo-differential Operators by : Louis Nirenberg

Download or read book Pseudo-differential Operators written by Louis Nirenberg and published by Springer Science & Business Media. This book was released on 2011-06-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: S. Agmon: Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators.- J. Bokobza-Haggiag: Une définition globale des opérateurs pseudo-différentiels sur une variété différentiable.- L. Boutet de Monvel: Pseudo-differential operators and analytic function.- A. Calderon: A priori estimates for singular integral operators.- B.F. Jones: Characterization of spaces of Bessel potentials related to the heat equation.- J.J. Kohn: Pseudo-differential operators and non-elliptic problems.- R.T. Seeley: Topics in pseudo-differential operators.- I.M. E. Shamir: Boundary value problems for elliptic convolution systems.- Singer: Elliptic operators on manifolds.

Degenerate Elliptic Equations

Author : Serge Levendorskii
Publisher : Springer Science & Business Media
ISBN 13 : 9401712158
Total Pages : 442 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Degenerate Elliptic Equations by : Serge Levendorskii

Download or read book Degenerate Elliptic Equations written by Serge Levendorskii and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.

Pseudodifferential Operators (PMS-34)

Author : Michael Eugene Taylor
Publisher : Princeton University Press
ISBN 13 : 1400886104
Total Pages : 465 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Pseudodifferential Operators (PMS-34) by : Michael Eugene Taylor

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 465 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.

Wave Factorization of Elliptic Symbols: Theory and Applications

Author : V. Vasil'ev
Publisher : Springer Science & Business Media
ISBN 13 : 9401594481
Total Pages : 184 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Wave Factorization of Elliptic Symbols: Theory and Applications by : V. Vasil'ev

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.

Linear Elliptic Differential Systems and Eigenvalue Problems

Author : Gaetano Fichera
Publisher : Springer
ISBN 13 : 3540371346
Total Pages : 183 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Linear Elliptic Differential Systems and Eigenvalue Problems by : Gaetano Fichera

Download or read book Linear Elliptic Differential Systems and Eigenvalue Problems written by Gaetano Fichera and published by Springer. This book was released on 2006-11-14 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Equations in Polyhedral Domains

Author : V. G. Maz_i_a
Publisher : American Mathematical Soc.
ISBN 13 : 0821849832
Total Pages : 618 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Elliptic Equations in Polyhedral Domains by : V. G. Maz_i_a

Download or read book Elliptic Equations in Polyhedral Domains written by V. G. Maz_i_a and published by American Mathematical Soc.. This book was released on 2010-04-22 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.

Partial Differential Equations IX

Author : M.S. Agranovich
Publisher : Springer
ISBN 13 : 9783642081699
Total Pages : 284 pages
Book Rating : 4.0/5 (816 download)

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Book Synopsis Partial Differential Equations IX by : M.S. Agranovich

Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer. This book was released on 2010-12-01 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.

Functional Calculus of Pseudodifferential Boundary Problems

Author : Gerd Grubb
Publisher : Springer Science & Business Media
ISBN 13 : 9780817637385
Total Pages : 544 pages
Book Rating : 4.6/5 (373 download)

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Book Synopsis Functional Calculus of Pseudodifferential Boundary Problems by : Gerd Grubb

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.

Partial Differential Equations VI

Author : Yu.V. Egorov
Publisher : Springer Science & Business Media
ISBN 13 : 3662092093
Total Pages : 332 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Partial Differential Equations VI by : Yu.V. Egorov

Download or read book Partial Differential Equations VI written by Yu.V. Egorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject.

Pseudodifferential Operators and Applications

Author : Francois Treves
Publisher : American Mathematical Soc.
ISBN 13 : 0821814699
Total Pages : 311 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Pseudodifferential Operators and Applications by : Francois Treves

Download or read book Pseudodifferential Operators and Applications written by Francois Treves and published by American Mathematical Soc.. This book was released on 1985 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings of the Symposium on Pseudodifferential Operators and Fourier Integral Operators with Applications to Partial Differential Equations held at the University of Notre Dame, Notre Dame, Indiana, April 2-5, 1984"--T.p. verso.

Second-Order Equations With Nonnegative Characteristic Form

Author : O. Oleinik
Publisher : Springer Science & Business Media
ISBN 13 : 1468489658
Total Pages : 265 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Second-Order Equations With Nonnegative Characteristic Form by : O. Oleinik

Download or read book Second-Order Equations With Nonnegative Characteristic Form written by O. Oleinik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second order equations with nonnegative characteristic form constitute a new branch of the theory of partial differential equations, having arisen within the last 20 years, and having undergone a particularly intensive development in recent years. An equation of the form (1) is termed an equation of second order with nonnegative characteristic form on a set G, kj if at each point x belonging to G we have a (xHk~j ~ 0 for any vector ~ = (~l' ... '~m)' In equation (1) it is assumed that repeated indices are summed from 1 to m, and x = (x l' ••• , x ). Such equations are sometimes also called degenerating m elliptic equations or elliptic-parabolic equations. This class of equations includes those of elliptic and parabolic types, first order equations, ultraparabolic equations, the equations of Brownian motion, and others. The foundation of a general theory of second order equations with nonnegative characteristic form has now been established, and the purpose of this book is to pre sent this foundation. Special classes of equations of the form (1), not coinciding with the well-studied equations of elliptic or parabolic type, were investigated long ago, particularly in the paper of Picone [105], published some 60 years ago.

Tools for PDE

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
ISBN 13 : 0821843788
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tools for PDE by : Michael E. Taylor

Download or read book Tools for PDE written by Michael E. Taylor and published by American Mathematical Soc.. This book was released on 2000 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing three related tools that are useful in the analysis of partial differential equations (PDEs) arising from the classical study of singular integral operators, this text considers pseudodifferential operators, paradifferential operators, and layer potentials.

Pseudo-Differential Operators, Generalized Functions and Asymptotics

Author : Shahla Molahajloo
Publisher : Springer Science & Business Media
ISBN 13 : 3034805853
Total Pages : 371 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Pseudo-Differential Operators, Generalized Functions and Asymptotics by : Shahla Molahajloo

Download or read book Pseudo-Differential Operators, Generalized Functions and Asymptotics written by Shahla Molahajloo and published by Springer Science & Business Media. This book was released on 2013-02-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.