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Second Order Equations With Nonnegative Characteristic Form

  • O. A. Oleĭnik
  • E. V. Radkevič

Table of contents

  1. Front Matter
    Pages i-vii
  2. O. A. Oleĭnik, E. V. Radkevič
    Pages 1-14
  3. O. A. Oleĭnik, E. V. Radkevič
    Pages 15-113
  4. O. A. Oleĭnik, E. V. Radkevič
    Pages 208-249
  5. Back Matter
    Pages 251-259

About this book

Introduction

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.

Keywords

Brownian motion Hilbert space Smooth function character class derivative development differential equation equation form partial differential equation pseudodifferential operator set types

Authors and affiliations

  • O. A. Oleĭnik
    • 1
  • E. V. Radkevič
    • 2
  1. 1.Moscow State UniversityMoscowUSSR
  2. 2.Institute for Problems of MechanicsAcademy of Sciences of the USSRMoscowUSSR

Bibliographic information