Partial Differential Equations Of Elliptic Type

Author : C. Miranda
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642877735

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Partial Differential Equations of Elliptic Type by C. Miranda Pdf

In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo sition, in some cases in summary form, of the various techniques used in the study of these equations.

Author : Angelo Alvino,Eugene Fabes,Giorgio Talenti
Publisher : Cambridge University Press
Page : 248 pages
File Size : 40,5 Mb
Release : 1994-08-26
Category : Mathematics
ISBN : 0521460484

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Partial Differential Equations of Elliptic Type by Angelo Alvino,Eugene Fabes,Giorgio Talenti Pdf

This is a conference proceedings volume covering the latest advances in partial differential equations of elliptic type. All workers on partial differential equations will find this book contains much valuable information.

Author : Qing Han,Fanghua Lin
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 44,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853139

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Elliptic Partial Differential Equations by Qing Han,Fanghua Lin Pdf

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.

Author : Carlo Miranda
Publisher : Springer
Page : 372 pages
File Size : 46,7 Mb
Release : 1970-01-01
Category : Mathematics
ISBN : 3662348195

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Partial Differential Equations of Elliptic Type by Carlo Miranda Pdf

Author : D. Gilbarg,N. S. Trudinger
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 51,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783642963797

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Elliptic Partial Differential Equations of Second Order by D. Gilbarg,N. S. Trudinger Pdf

This volume is intended as an essentially self contained exposition of portions of the theory of second order quasilinear elliptic partial differential equations, with emphasis on the Dirichlet problem in bounded domains. It grew out of lecture notes for graduate courses by the authors at Stanford University, the final material extending well beyond the scope of these courses. By including preparatory chapters on topics such as potential theory and functional analysis, we have attempted to make the work accessible to a broad spectrum of readers. Above all, we hope the readers of this book will gain an appreciation of the multitude of ingenious barehanded techniques that have been developed in the study of elliptic equations and have become part of the repertoire of analysis. Many individuals have assisted us during the evolution of this work over the past several years. In particular, we are grateful for the valuable discussions with L. M. Simon and his contributions in Sections 15.4 to 15.8; for the helpful comments and corrections of J. M. Cross, A. S. Geue, J. Nash, P. Trudinger and B. Turkington; for the contributions of G. Williams in Section 10.5 and of A. S. Geue in Section 10.6; and for the impeccably typed manuscript which resulted from the dedicated efforts oflsolde Field at Stanford and Anna Zalucki at Canberra. The research of the authors connected with this volume was supported in part by the National Science Foundation.

Author : Andreĭ Vasilʹevich Bit︠s︡adze
Publisher : CRC Press
Page : 532 pages
File Size : 51,7 Mb
Release : 1988
Category : Mathematics
ISBN : 2881246621

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Some Classes of Partial Differential Equations by Andreĭ Vasilʹevich Bit︠s︡adze Pdf

A systematic examination of classical and non-classical problems for linear partial differential equations and systems of elliptic, hyperbolic and mixed types. Among a number of difficult problems addressed are the Dirichlet and oblique derivative problems for non- uniformly elliptic equations and non-strongly elliptic systems and the Cauchy and Darloux problems for non-strongly hyperbolic systems and hyperbolic equations with parabolic degeneracy on the boundary. Written at a level suitable for undergraduate and graduate students and researchers. Individual price, $89. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Thomas H. Otway
Publisher : Springer
Page : 128 pages
File Size : 49,5 Mb
Release : 2015-07-08
Category : Mathematics
ISBN : 9783319197616

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Elliptic–Hyperbolic Partial Differential Equations by Thomas H. Otway Pdf

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

Author : Angelo Alvino
Publisher : Unknown
Page : 223 pages
File Size : 44,9 Mb
Release : 1994
Category : Electronic
ISBN : OCLC:657945515

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Partial Differential Equations of Elliptic Type (1992 by Angelo Alvino Pdf

Author : Avner Friedman
Publisher : Courier Corporation
Page : 369 pages
File Size : 41,7 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780486318264

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Partial Differential Equations of Parabolic Type by Avner Friedman Pdf

With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

Author : Jan Malý,William P. Ziemer
Publisher : American Mathematical Soc.
Page : 309 pages
File Size : 54,8 Mb
Release : 1997
Category : Boundary value problems
ISBN : 9780821803356

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Fine Regularity of Solutions of Elliptic Partial Differential Equations by Jan Malý,William P. Ziemer Pdf

The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.

Author : Wolfgang Hackbusch
Publisher : Springer
Page : 455 pages
File Size : 49,5 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783662549612

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Elliptic Differential Equations by Wolfgang Hackbusch Pdf

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Author : E. M. Landis
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 54,7 Mb
Release : 1997-12-02
Category : Mathematics
ISBN : 0821897810

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Second Order Equations of Elliptic and Parabolic Type by E. M. Landis Pdf

Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity. The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.

Author : Stanley J. Farlow
Publisher : Courier Corporation
Page : 414 pages
File Size : 50,6 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780486134734

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Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow Pdf

Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.

Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 54,9 Mb
Release : 2012-11-13
Category : Mathematics
ISBN : 9781461448099

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Partial Differential Equations by Jürgen Jost Pdf

This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.

Author : E. T. Copson
Publisher : CUP Archive
Page : 292 pages
File Size : 41,5 Mb
Release : 1975-10-02
Category : Mathematics
ISBN : 0521098939

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Partial Differential Equations by E. T. Copson Pdf

In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its relevance in several important respects. Many branches of classical analysing have their origins in the rigourous discussion of problems in applies mathematics and theoretical physics, and the classical treatment of the theory of partial differential equations still provides the best method of treating many physical problems. A knowledge of the classical theory is essential for pure mathematics who intend to undertake research in this field, whatever approach they ultimately adopt. The numerical analyst needs a knowledge of classical theory in order to decide whether a problem has a unique solution or not.