Phragmèn-Lindelöf and Comparison Theorems for Elliptic-Parabolic Differential Equations
J. K. Oddson · Canadian Journal of Mathematics · 1967
Theorems of Phragmèn-Lindelöf type and other related results for solutions of elliptic-parabolic equations have been given by numerous authors in recent years. Many of these results are based upon the maximum principle and the use of auxiliary comparison functions which are constructed as supersolutions of the equations under various conditions on the coefficients. In this paper we present an axiomatized treatment of these topics, replacing specific hypotheses on the nature of the coefficients of the equations by a single assumption concerning the maximum principle and another concerning the existence of positive supersolutions, in terms of which the theorems are stated.