Elliptic Boundary Value Problems On Corner Domains PDF Download
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Author | : Monique Dauge |
Publisher | : Springer |
Total Pages | : 266 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540459421 |
Download Elliptic Boundary Value Problems on Corner Domains Book in PDF, ePub and Kindle
This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and semi-Fredholm properties of induced operators are completely characterized. By specially choosing the classes of operators and domains and the functional spaces used, precise and general results may be obtained on the smoothness and asymptotics of solutions. A new type of characteristic condition is introduced which involves the spectrum of associated operator pencils and some ideals of polynomials satisfying some boundary conditions on cones. The methods involve many perturbation arguments and a new use of Mellin transform. Basic knowledge about BVP on smooth domains in Sobolev spaces is the main prerequisite to the understanding of this book. Readers interested in the general theory of corner domains will find here a new basic theory (new approaches and results) as well as a synthesis of many already known results; those who need regularity conditions and descriptions of singularities for numerical analysis will find precise statements and also a means to obtain further one in many explicit situtations.
Author | : Monique Dauge |
Publisher | : |
Total Pages | : 276 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9783662165232 |
Download Elliptic Boundary Value Problems on Corner Domains Book in PDF, ePub and Kindle
Author | : Pierre Grisvard |
Publisher | : SIAM |
Total Pages | : 430 |
Release | : 1985-01-01 |
Genre | : Mathematics |
ISBN | : 9781611972030 |
Download Elliptic Problems in Nonsmooth Domains Book in PDF, ePub and Kindle
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.
Author | : Monique Dauge |
Publisher | : |
Total Pages | : 257 |
Release | : 1988 |
Genre | : Dominios con esquinas |
ISBN | : |
Download Elliptic boundary value : problems an corner domains : smoothness and asymptotics of solutions Book in PDF, ePub and Kindle
Author | : Vladimir Kozlov |
Publisher | : American Mathematical Soc. |
Total Pages | : 426 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821807544 |
Download Elliptic Boundary Value Problems in Domains with Point Singularities Book in PDF, ePub and Kindle
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 | : 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 | : Michail Borsuk |
Publisher | : Elsevier |
Total Pages | : 538 |
Release | : 2006-01-12 |
Genre | : Mathematics |
ISBN | : 0080461735 |
Download Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains Book in PDF, ePub and Kindle
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
Author | : Martin Costabel |
Publisher | : CRC Press |
Total Pages | : 320 |
Release | : 1994-10-25 |
Genre | : Mathematics |
ISBN | : 9780824793203 |
Download Boundary Value Problems and Integral Equations in Nonsmooth Domains Book in PDF, ePub and Kindle
Based on the International Conference on Boundary Value Problems and lntegral Equations In Nonsmooth Domains held recently in Luminy, France, this work contains strongly interrelated, refereed papers that detail the latest findings in the fields of nonsmooth domains and corner singularities. Two-dimensional polygonal or Lipschitz domains, three-dimensional polyhedral corners and edges, and conical points in any dimension are examined.
Author | : Sergey Nazarov |
Publisher | : Walter de Gruyter |
Total Pages | : 537 |
Release | : 2011-06-01 |
Genre | : Mathematics |
ISBN | : 3110848910 |
Download Elliptic Problems in Domains with Piecewise Smooth Boundaries Book in PDF, ePub and Kindle
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Author | : Guo Chun Wen |
Publisher | : Chapman & Hall/CRC |
Total Pages | : 432 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Download Boundary Value Problems for Elliptic Equations and Systems Book in PDF, ePub and Kindle
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.