Oblique Derivative Problems For Elliptic Equations In Conical Domains
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Oblique Derivative Problems For Elliptic Equations In Conical Domains
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Author : Mikhail Borsuk
language : en
Publisher: Springer Nature
Release Date : 2023-05-31
Oblique Derivative Problems For Elliptic Equations In Conical Domains written by Mikhail Borsuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Mathematics categories.
The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.
Oblique Derivative Problems For Elliptic Equations In Conical Domains
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Author : Mikhail Borsuk
language : en
Publisher:
Release Date : 2023
Oblique Derivative Problems For Elliptic Equations In Conical Domains written by Mikhail Borsuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.
Oblique Derivative Problems For Elliptic Equations
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Author : Gary M. Lieberman
language : en
Publisher: World Scientific
Release Date : 2013
Oblique Derivative Problems For Elliptic Equations written by Gary M. Lieberman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.
This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. The author begins the book with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. The final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading.
Oblique Derivative Problems For Elliptic Equations
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Author : Gary M Lieberman
language : en
Publisher: World Scientific
Release Date : 2013-03-26
Oblique Derivative Problems For Elliptic Equations written by Gary M Lieberman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-26 with Mathematics categories.
This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. The author begins the book with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. The final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading.
The Oblique Derivative Problem Of Potential Theory
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Author : A.T. Yanushauakas
language : en
Publisher: Springer
Release Date : 2013-05-14
The Oblique Derivative Problem Of Potential Theory written by A.T. Yanushauakas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-14 with Mathematics categories.
An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob lems, whose investigation reduces, as a rule, to the study of singular integral equa tions, where the Fredholm alternative is violated for these problems. Thanks to de velopments in the theory of one-dimensional singular integral equations [28, 29], boundary problems for elliptic equations with two independent variables have been completely studied at the present time [13, 29], which cannot be said about bound ary problems for elliptic equations with many independent variables. A number of important questions in this area have not yet been solved, since one does not have sufficiently general methods for investigating them. Among the boundary problems of great interest is the oblique derivative problem for harmonic functions, which can be formulated as follows: In a domain D with sufficiently smooth boundary r find a harmonic function u(X) which, on r, satisfies the condition n n ~ au ~ . . . :;. . ai (X) ax. = f (X), . . . :;. . [ai (X)]2 = 1, i=l t i=l where aI, . . . , an,fare sufficiently smooth functions defined on r. Obviously the left side of the boundary condition is the derivative of the function u(X) in the direction of the vector P(X) with components al (X), . . . , an(X).
Elliptic Boundary Value Problems Of Second Order In Piecewise Smooth Domains
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Author : Michail Borsuk
language : en
Publisher: Elsevier
Release Date : 2006-01-12
Elliptic Boundary Value Problems Of Second Order In Piecewise Smooth Domains written by Michail Borsuk and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-12 with Mathematics categories.
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.
Transmission Problems For Elliptic Second Order Equations In Non Smooth Domains
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Author : Mikhail Borsuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02
Transmission Problems For Elliptic Second Order Equations In Non Smooth Domains written by Mikhail Borsuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Mathematics categories.
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.
Boundary Value Problems For Second Order Elliptic Equations
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Author : A.V. Bitsadze
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Boundary Value Problems For Second Order Elliptic Equations written by A.V. Bitsadze and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
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.
Elliptic Boundary Value Problems In Domains With Point Singularities
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Author : V. A. Kozlov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Elliptic Boundary Value Problems In Domains With Point Singularities written by V. A. Kozlov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Boundary value problems categories.
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
The Degenerate Oblique Derivative Problem For Elliptic And Parabolic Equations Paper Only See 3527401121
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Author : Petar R. Popivanov
language : en
Publisher: Wiley-VCH
Release Date : 1997-04-17
The Degenerate Oblique Derivative Problem For Elliptic And Parabolic Equations Paper Only See 3527401121 written by Petar R. Popivanov and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-17 with Mathematics categories.