Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - February 1986 - Volume 29, Issue 01  

Research Article

On the strong maximum principle for parabolic differential equations

Wolfgang Waltera1

a1 Mathematisches Institut, Universitāt Karlsruhe

In a recent paper [2], D. Colton has given a new proof for the strong maximum principle with regard to the heat equation ut = Δu. His proof depends on the analyticity (in x) of solutions. For this reason it does not carry over to the equation

S0013091500017442_eqnU1

or to more general equations. But in order to tread mildly nonlinear equations such asut = Δu + f(u) which are important in many applications, it is essential to have the strong maximum principle at least for equation (*). It should also be said that this proof uses nontrivial facts about the heat equation.

(Received February 04 1985)