Unique Continuation Property of Non-Positive Weak Subsolutions for Parabolic Equations of Higher Order

Abstract

When L is a parabolic differential operator of second order, Nirenberg [6] proved the maximum principle for the function u which has second order continuous derivatives and satisfies Lu≧0. Recently Friedman [2] has proved the maximum principle for the measurable function satisfying Lu≧O in the wide sense. This function is named a weakly L-subparabolic function. On the other hand, Littman [5] earlier than Friedman, has defined a weakly A- subharmonic function for an elliptic differential operator A of second order and has showed the maximum principle for it.