Advertisement

Fritz John pp 107-110 | Cite as

A Note on the Maximum Principle for Elliptic Differential Equations

  • Fritz John
Chapter
Part of the Contemporary Mathematicians book series (CM)

Abstract

Let u( x 1, … , x n ) denote a twice continuously differentiate function of x 1, … , x n in some region R. We write ∂u/∂x i = u i , 2 u/∂x i ∂x k = u ik , and occasionally (x) for (x 1, … , x n ). A point (c) = (c 1, … , c n ) of R may be called a proper maximum of u, if u i (c) = 0 for i = 1, · · · n,
$$\sum\limits_{i,k} {{u_{ik}}(c)} {\xi _i}{\xi _k} < 0$$
for all (ξ 1, …, ξ n ) ≠ (0, …, 0).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Fritz John

There are no affiliations available

Personalised recommendations