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Lectures On Elliptic Boundary Value Problems
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Book Synopsis Lectures on Elliptic Boundary Value Problems by : Shmuel Agmon
Download or read book Lectures on Elliptic Boundary Value Problems written by Shmuel Agmon and published by American Mathematical Soc.. This book was released on 2010-02-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is a new edition of a book originally published in 1965, presents an introduction to the theory of higher-order elliptic boundary value problems. The book contains a detailed study of basic problems of the theory, such as the problem of existence and regularity of solutions of higher-order elliptic boundary value problems. It also contains a study of spectral properties of operators associated with elliptic boundary value problems. Weyl's law on the asymptotic distribution of eigenvalues is studied in great generality.
Book Synopsis Lectures on Elliptic and Parabolic Equations in Holder Spaces by : Nikolaĭ Vladimirovich Krylov
Download or read book Lectures on Elliptic and Parabolic Equations in Holder Spaces written by Nikolaĭ Vladimirovich Krylov and published by American Mathematical Soc.. This book was released on 1996 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.
Book Synopsis Lectures on Elliptic and Parabolic Equations in Sobolev Spaces by : Nikolaĭ Vladimirovich Krylov
Download or read book Lectures on Elliptic and Parabolic Equations in Sobolev Spaces written by Nikolaĭ Vladimirovich Krylov and published by American Mathematical Soc.. This book was released on 2008 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.
Book Synopsis Lectures on Linear Partial Differential Equations by : Grigoriĭ Ilʹich Eskin
Download or read book Lectures on Linear Partial Differential Equations written by Grigoriĭ Ilʹich Eskin and published by American Mathematical Soc.. This book was released on 2011 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory.
Book Synopsis Lectures on Elliptic Boundary Value Problems by :
Download or read book Lectures on Elliptic Boundary Value Problems written by and published by American Mathematical Soc.. This book was released on 1965 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Differential Equations by : Philip L. Korman
Download or read book Lectures on Differential Equations written by Philip L. Korman and published by American Mathematical Soc.. This book was released on 2019-08-30 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Differential Equations provides a clear and concise presentation of differential equations for undergraduates and beginning graduate students. There is more than enough material here for a year-long course. In fact, the text developed from the author's notes for three courses: the undergraduate introduction to ordinary differential equations, the undergraduate course in Fourier analysis and partial differential equations, and a first graduate course in differential equations. The first four chapters cover the classical syllabus for the undergraduate ODE course leavened by a modern awareness of computing and qualitative methods. The next two chapters contain a well-developed exposition of linear and nonlinear systems with a similarly fresh approach. The final two chapters cover boundary value problems, Fourier analysis, and the elementary theory of PDEs. The author makes a concerted effort to use plain language and to always start from a simple example or application. The presentation should appeal to, and be readable by, students, especially students in engineering and science. Without being excessively theoretical, the book does address a number of unusual topics: Massera's theorem, Lyapunov's inequality, the isoperimetric inequality, numerical solutions of nonlinear boundary value problems, and more. There are also some new approaches to standard topics including a rethought presentation of series solutions and a nonstandard, but more intuitive, proof of the existence and uniqueness theorem. The collection of problems is especially rich and contains many very challenging exercises. Philip Korman is professor of mathematics at the University of Cincinnati. He is the author of over one hundred research articles in differential equations and the monograph Global Solution Curves for Semilinear Elliptic Equations. Korman has served on the editorial boards of Communications on Applied Nonlinear Analysis, Electronic Journal of Differential Equations, SIAM Review, an\ d Differential Equations and Applications.
Book Synopsis Hierarchical Matrices by : Mario Bebendorf
Download or read book Hierarchical Matrices written by Mario Bebendorf and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions. The theory is supported by many numerical experiments from real applications.
Book Synopsis Elliptic Boundary Value Problems in Domains with Point Singularities by : Vladimir Kozlov
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
Book Synopsis Elliptic Partial Differential Equations by : Qing Han
Download or read book Elliptic Partial Differential Equations written by Qing Han and published by American Mathematical Soc.. This book was released on 2011 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
Book Synopsis Boundary Value Problems by : F. D. Gakhov
Download or read book Boundary Value Problems written by F. D. Gakhov and published by Elsevier. This book was released on 2014-07-10 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.
Book Synopsis Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains by : Mikhail S. Agranovich
Download or read book Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains written by Mikhail S. Agranovich and published by Springer. This book was released on 2015-05-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.
Book Synopsis Index Theory of Elliptic Boundary Problems by : Stephan Rempel
Download or read book Index Theory of Elliptic Boundary Problems written by Stephan Rempel and published by Walter de Gruyter GmbH & Co KG. This book was released on 1982-12-31 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Index Theory of Elliptic Boundary Problems".
Book Synopsis Lectures on Elliptic Partial Differential Equations by : Jacques-Louis Lions
Download or read book Lectures on Elliptic Partial Differential Equations written by Jacques-Louis Lions and published by . This book was released on 1967 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Conference on Differential & Difference Equations and Applications by : Ravi P. Agarwal
Download or read book Proceedings of the Conference on Differential & Difference Equations and Applications written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 1266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Oblique Derivative Problems for Elliptic Equations by : Gary M. Lieberman
Download or read book Oblique Derivative Problems for Elliptic Equations written by Gary M. Lieberman and published by World Scientific. This book was released on 2013 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elliptic Differential Equations by : W. Hackbusch
Download or read book Elliptic Differential Equations written by W. Hackbusch and published by Springer Science & Business Media. This book was released on 1992 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR
Book Synopsis Green's Functions and Boundary Value Problems by : Ivar Stakgold
Download or read book Green's Functions and Boundary Value Problems written by Ivar Stakgold and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
