Elliptic Boundary Value Problems Of Second Order In Piecewise Smooth Domains
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Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains
Author | : Michail Borsuk,Vladimir Kondratiev |
Publsiher | : Elsevier |
Total Pages | : 538 |
Release | : 2006-01-12 |
Genre | : Mathematics |
ISBN | : 0080461735 |
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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.
Elliptic Problems in Domains with Piecewise Smooth Boundaries
Author | : Sergey Nazarov,Boris A. Plamenevsky |
Publsiher | : Walter de Gruyter |
Total Pages | : 537 |
Release | : 2011-06-01 |
Genre | : Mathematics |
ISBN | : 9783110848915 |
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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
Transmission Problems for Elliptic Second Order Equations in Non Smooth Domains
Author | : Mikhail Borsuk |
Publsiher | : Springer Science & Business Media |
Total Pages | : 223 |
Release | : 2010-09-02 |
Genre | : Mathematics |
ISBN | : 9783034604772 |
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This book investigates the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges, considering this problem both for linear and quasi-linear equations.
Elliptic Boundary Value Problems in Domains with Point Singularities
Author | : V. A. Kozlov,V. G. Mazʹi︠a︡,J. Rossmann,Jürgen Rossmann |
Publsiher | : American Mathematical Soc. |
Total Pages | : 426 |
Release | : 1997 |
Genre | : Boundary value problems |
ISBN | : 9780821807545 |
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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
Elliptic Boundary Value Problems on Corner Domains
Author | : Monique Dauge |
Publsiher | : Springer |
Total Pages | : 266 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540459422 |
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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.
Boundary Value Problems in Non smooth Domains
Author | : Pierre Grisvard |
Publsiher | : Unknown |
Total Pages | : 350 |
Release | : 1980 |
Genre | : Boundary value problems |
ISBN | : UOM:39015015720645 |
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Elliptic Equations in Polyhedral Domains
Author | : V. G. Maz_i_a,Jrgen Rossmann |
Publsiher | : American Mathematical Soc. |
Total Pages | : 618 |
Release | : 2010-04-22 |
Genre | : Mathematics |
ISBN | : 9780821849835 |
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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.
Boundary Value Problems for Second Order Elliptic Equations
Author | : Andreĭ Vasilʹevich Bit︠s︡adze |
Publsiher | : Unknown |
Total Pages | : 222 |
Release | : 1968 |
Genre | : Mathematics |
ISBN | : UCAL:B4405981 |
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