Download or read book Boundary Value Problems Associated with First Order Elliptic Systems in the Plane written by R. P. Gilbert and published by . This book was released on 1981 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Boundary value Problems with Free Boundaries for Elliptic Systems of Equations written by Valentin Nikolaevich Monakhov and published by American Mathematical Soc.. This book was released on 1983 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations written by Vladimir Kozlov and published by American Mathematical Soc.. This book was released on 2001 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Riemann Boundary Value Problems for Certain Linear Elliptic Systems in the Plane written by and published by . This book was released on 1977 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The partial differential equations which occur in the theory of elastic plates and shells are among those which may be reduced to a first order elliptic system. Under certain regularity conditions for the coefficients, a Beltrami transformation exists taking the general first-order, elliptic systems into a normal-Douglis-form. This form can be further simplified, and more concisely represented by utilizing the algebra of hypercomplex numbers. The theory of solutions to these linear systems is known as generalized hyperanalytic function theory. The present work deals with Riemann boundary value problems for linear systems. It is shown that every solution of the homogeneous boundary value problem may be written as a linear combination of special solutions resembling Bers generating pairs. The nonhomogeneous solution is represented as a homogeneous solution plus a particular solution which is given as an integral representation using a generalized Cauchy kernel.
Download or read book First Order Elliptic Systems A Function Theoretic Approach written by Buchanan and published by Academic Press. This book was released on 1983-07-19 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Order Elliptic Systems: A Function Theoretic Approach
Download or read book Boundary Value Problems Governed by Second Order Elliptic Systems written by David L. Clements and published by Pitman Advanced Publishing Program. This book was released on 1981 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elliptic Boundary Value Problems with Fractional Regularity Data written by Alex Amenta and published by American Mathematical Soc.. This book was released on 2018-04-03 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Degenerate and Other Problems written by Abduhamid Dzhuraev and published by CRC Press. This book was released on 2020-10-07 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Monograph contains a collection of problems arising in partial differential equations investigated by means of complex analysis approached in elementary ways.
Download or read book Boundary Value Problems for Elliptic Equations and Systems written by Guo Chun Wen and published by Longman Scientific and Technical. This book was released on 1990 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plane Ellipticity and Related Problems written by Robert P. Gilbert and published by American Mathematical Soc.. This book was released on 1982-12-31 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Boundary Value Problems of Elliptic Systems in the Plane written by Wolfgang L. Wendland and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elliptic Problems in Nonsmooth Domains written by Pierre Grisvard and published by SIAM. This book was released on 1985-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text focuses on elliptic boundary value problems in domains with nonsmooth boundaries and on problems with mixed boundary conditions. Its contents are essential for an understanding of the behavior of numerical methods for partial differential equations (PDEs) on two-dimensional domains with corners. Elliptic problems in nonsmooth domains: provides a careful and self-contained development of Sobolev spaces on nonsmooth domains, develops a comprehensive theory for second-order elliptic boundary value problems, and addresses fourth-order boundary value problems and numerical treatment of singularities.
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
Download or read book Introductory Numerical Analysis of Elliptic Boundary Value Problems written by Donald Greenspan and published by . This book was released on 1965 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
