Second Order Equations with Nonnegative Characteristic Form - Hardcover

Oleinik, O. A.; Radkevic, E. V.

Hardcover

ISBN 10: 0306307510 ISBN 13: 9780306307515

Publisher: Kluwer Academic/Plenum Publishers, 1973

Synopsis

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.

Edition details

• Publisher: Kluwer Academic/Plenum Publishers
• Publication date: 1973
• Language: English
• ISBN 10: 0306307510
• ISBN 13: 9780306307515
• Binding: Hardcover
• Number of pages: 259