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Introduction

Part of the Applied Mathematical Sciences book series (AMS, volume 1)

Abstract

A partial differential equation for a function u(x, y,…) with partial derivatives ux, uy, uxx, uxy,… is a relation of the form
$$ F(x,y,...,u,{u_x},{u_y},{u_{xx}},...,) = 0 $$
(1)
, where F is a given function of the variables x, y,..., u, ux, uy, uxx,... Only a finite number of derivatives shall occur. Needless to say, a function u(x, y,...) is said to be a solution of (1), if in some region of the space of its independent variables, the function and its derivatives satisfy the equation identically in x,y,... .

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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • F. John
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

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