Second Order Equations Of Elliptic And Parabolic Type
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Author | : E. M. Landis |
Publisher | : American Mathematical Soc. |
Total Pages | : 224 |
Release | : 1997-12-02 |
Genre | : Mathematics |
ISBN | : 9780821897812 |
Download Second Order Equations of Elliptic and Parabolic Type Book in PDF, Epub and Kindle
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 | : Evgeniĭ Mikhaĭlovich Landis |
Publisher | : American Mathematical Soc. |
Total Pages | : 203 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9780821808573 |
Download Second Order Equations of Elliptic and Parabolic Type Book in PDF, Epub and Kindle
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 | : O. Oleinik |
Publisher | : Springer Science & Business Media |
Total Pages | : 265 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468489658 |
Download Second-Order Equations With Nonnegative Characteristic Form Book in PDF, Epub and Kindle
Second order equations with nonnegative characteristic form constitute a new branch of the theory of partial differential equations, having arisen within the last 20 years, and having undergone a particularly intensive development in recent years. An equation of the form (1) is termed an equation of second order with nonnegative characteristic form on a set G, kj if at each point x belonging to G we have a (xHk~j ~ 0 for any vector ~ = (~l' ... '~m)' In equation (1) it is assumed that repeated indices are summed from 1 to m, and x = (x l' ••• , x ). Such equations are sometimes also called degenerating m elliptic equations or elliptic-parabolic equations. This class of equations includes those of elliptic and parabolic types, first order equations, ultraparabolic equations, the equations of Brownian motion, and others. The foundation of a general theory of second order equations with nonnegative characteristic form has now been established, and the purpose of this book is to pre sent this foundation. Special classes of equations of the form (1), not coinciding with the well-studied equations of elliptic or parabolic type, were investigated long ago, particularly in the paper of Picone [105], published some 60 years ago.
Author | : Avner Friedman |
Publisher | : Courier Corporation |
Total Pages | : 369 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 0486318265 |
Download Partial Differential Equations of Parabolic Type Book in PDF, Epub and Kindle
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 | : Gary M. Lieberman |
Publisher | : World Scientific |
Total Pages | : 472 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9789810228835 |
Download Second Order Parabolic Differential Equations Book in PDF, Epub and Kindle
Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Author | : Luca Lorenzi |
Publisher | : CRC Press |
Total Pages | : 350 |
Release | : 2021-01-06 |
Genre | : Mathematics |
ISBN | : 0429557663 |
Download Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations Book in PDF, Epub and Kindle
Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations aims to propose a unified approach to elliptic and parabolic equations with bounded and smooth coefficients. The book will highlight the connections between these equations and the theory of semigroups of operators, while demonstrating how the theory of semigroups represents a powerful tool to analyze general parabolic equations. Features Useful for students and researchers as an introduction to the field of partial differential equations of elliptic and parabolic types Introduces the reader to the theory of operator semigroups as a tool for the analysis of partial differential equations
Author | : Antonino Maugeri |
Publisher | : Wiley-VCH |
Total Pages | : 266 |
Release | : 2000-12-13 |
Genre | : Mathematics |
ISBN | : |
Download Elliptic and Parabolic Equations with Discontinuous Coefficients Book in PDF, Epub and Kindle
This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.
Author | : N.V. Krylov |
Publisher | : Springer |
Total Pages | : 480 |
Release | : 1987-06-30 |
Genre | : Mathematics |
ISBN | : 9027722897 |
Download Nonlinear Elliptic and Parabolic Equations of the Second Order Book in PDF, Epub and Kindle
Author | : Olʹga A. Ladyženskaja |
Publisher | : American Mathematical Soc. |
Total Pages | : 74 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 9780821815731 |
Download Linear and Quasi-linear Equations of Parabolic Type Book in PDF, Epub and Kindle
Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Author | : A. V. Ivanov |
Publisher | : American Mathematical Soc. |
Total Pages | : 306 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 9780821830802 |
Download Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order Book in PDF, Epub and Kindle