Second-Order Equations With Nonnegative Characteristic Form

1. Front Matter

   Pages i-vii

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2. Introduction

   • O. A. Oleĭnik, E. V. Radkevič

   Pages 1-14

3. The First Boundary Value Problem

   • O. A. Oleĭnik, E. V. Radkevič

   Pages 15-113

4. On the Local Smoothness of Weak Solutions and Hypoellipticity of Second Order Differential Equations

   • O. A. Oleĭnik, E. V. Radkevič

   Pages 114-207

5. Additional Topics

   • O. A. Oleĭnik, E. V. Radkevič

   Pages 208-249

6. Back Matter

   Pages 251-259

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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.

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

• Moscow State University, Moscow, USSR

  O. A. Oleĭnik

• Institute for Problems of Mechanics, Academy of Sciences of the USSR, Moscow, USSR

  E. V. Radkevič

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