Abstract:
We prove the strong maximum principle for an analogue of parabolic operators for stratified sets. It is shown, that the solution of a parabolic equation on a stratified set with nonnegative right side can possess a local maximum inside of a stratified cylinder only if solution is a constant in some neighborhood of this maximum. In addition, we prove an analogue of the Hopf-Oleynik normal derivative lemma for stratified sets. We show that if the normal derivative of the solution of a parabolic equation on a stratified set with nonnegative right side exists in some maximum point on the lateral boundary of the cylinder and the boundary satisfies so-called hyperplane condition then this derivative is negative in this point.
Keywords:stratified set, strong maximum principle, lemma of normal derivative.
