Foreslået køb Second-Order Equations With Nonnegative Characteristic Form (Paperback) by Oleinik O. A. dPyKurPL

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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.