Boundary Value Problems For Elliptic Systems
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Author | : J. T. Wloka |
Publisher | : Cambridge University Press |
Total Pages | : 659 |
Release | : 1995-07-28 |
Genre | : Mathematics |
ISBN | : 0521430119 |
Download Boundary Value Problems for Elliptic Systems Book in PDF, Epub and Kindle
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 | : Valentin Nikolaevich Monakhov |
Publisher | : American Mathematical Soc. |
Total Pages | : 540 |
Release | : 1983 |
Genre | : Mathematics |
ISBN | : 9780821898079 |
Download Boundary-value Problems with Free Boundaries for Elliptic Systems of Equations Book in PDF, Epub and Kindle
This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.
Author | : William Charles Hector McLean |
Publisher | : Cambridge University Press |
Total Pages | : 376 |
Release | : 2000-01-28 |
Genre | : Mathematics |
ISBN | : 9780521663755 |
Download Strongly Elliptic Systems and Boundary Integral Equations Book in PDF, Epub and Kindle
This 2000 book provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains.
Author | : Charles A. Hayes |
Publisher | : |
Total Pages | : 114 |
Release | : 1942 |
Genre | : Differential equations, Linear |
ISBN | : |
Download Boundary Value Problems for Elliptic Systems of [linear] Partial Differential Equations Book in PDF, Epub and Kindle
Author | : A.V. Bitsadze |
Publisher | : Elsevier |
Total Pages | : 212 |
Release | : 2012-12-02 |
Genre | : Mathematics |
ISBN | : 0323162266 |
Download Boundary Value Problems For Second Order Elliptic Equations Book in PDF, Epub and Kindle
Applied Mathematics and Mechanics, Volume 5: Boundary Value Problems: For Second Order Elliptic Equations is a revised and augmented version of a lecture course on non-Fredholm elliptic boundary value problems, delivered at the Novosibirsk State University in the academic year 1964-1965. This seven-chapter text is devoted to a study of the basic linear boundary value problems for linear second order partial differential equations, which satisfy the condition of uniform ellipticity. The opening chapter deals with the fundamental aspects of the linear equations theory in normed linear spaces. This topic is followed by discussions on solutions of elliptic equations and the formulation of Dirichlet problem for a second order elliptic equation. A chapter focuses on the solution equation for the directional derivative problem. Another chapter surveys the formulation of the Poincaré problem for second order elliptic systems in two independent variables. This chapter also examines the theory of one-dimensional singular integral equations that allow the investigation of highly important classes of boundary value problems. The final chapter looks into other classes of multidimensional singular integral equations and related boundary value problems.
Author | : Guo Chun Wen |
Publisher | : Longman Scientific and Technical |
Total Pages | : 430 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Download Boundary Value Problems for Elliptic Equations and Systems Book in PDF, Epub and Kindle
Author | : Vladimir Kozlov |
Publisher | : American Mathematical Soc. |
Total Pages | : 449 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821827278 |
Download Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations Book in PDF, Epub and Kindle
This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: The first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems. Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented. Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems. Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator. Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order 2m in an angle. In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order 2 in an n-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $\mid {\Re} \lambda - m + /2n \mid \leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues. Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses.
Author | : J. R. BARNUM |
Publisher | : |
Total Pages | : 1 |
Release | : 1962 |
Genre | : |
ISBN | : |
Download General Boundary Value Problems for Elliptic Systems in Multi-dimengenerators by Means of Thermocouples Book in PDF, Epub and Kindle
Author | : Wenjie Gao |
Publisher | : |
Total Pages | : 192 |
Release | : 1988 |
Genre | : |
ISBN | : |
Download Boundary Value Problems on Lipschitz Domains for General Elliptic Systems Book in PDF, Epub and Kindle
Author | : Alex Amenta |
Publisher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 2018-04-03 |
Genre | : Mathematics |
ISBN | : 1470442507 |
Download Elliptic Boundary Value Problems with Fractional Regularity Data Book in PDF, Epub and Kindle
A co-publication of the AMS and Centre de Recherches Mathématiques In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The authors use the so-called “first order approach” which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.