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Second Order Equations of Elliptic and Parabolic Type

1997-12-02 Mathematics
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Release : 1997-12-02
Genre : Mathematics
Kind : eBook
Book Rating : 812/5 ( reviews)

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Book Synopsis Second Order Equations of Elliptic and Parabolic Type by : E. M. Landis

Download or read book Second Order Equations of Elliptic and Parabolic Type written by E. M. Landis. This book was released on 1997-12-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Second Order Equations of Elliptic and Parabolic Type

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 573/5 ( reviews)

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Book Synopsis Second Order Equations of Elliptic and Parabolic Type by : Evgeniĭ Mikhaĭlovich Landis

Download or read book Second Order Equations of Elliptic and Parabolic Type written by Evgeniĭ Mikhaĭlovich Landis. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Partial Differential Equations of Parabolic Type

2013-08-16 Mathematics
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Release : 2013-08-16
Genre : Mathematics
Kind : eBook
Book Rating : 265/5 ( reviews)

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Book Synopsis Partial Differential Equations of Parabolic Type by : Avner Friedman

Download or read book Partial Differential Equations of Parabolic Type written by Avner Friedman. This book was released on 2013-08-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Second-Order Equations With Nonnegative Characteristic Form

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 658/5 ( reviews)

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Book Synopsis Second-Order Equations With Nonnegative Characteristic Form by : O. Oleinik

Download or read book Second-Order Equations With Nonnegative Characteristic Form written by O. Oleinik. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Second Order Parabolic Differential Equations

1996 Mathematics
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Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : 835/5 ( reviews)

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Book Synopsis Second Order Parabolic Differential Equations by : Gary M. Lieberman

Download or read book Second Order Parabolic Differential Equations written by Gary M. Lieberman. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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