A note on the classical weak and strong maximum principles for linear parabolic partial differential inequalities

摘要: In this note, we highlight a difference in the conditions of classical weak maximum principle and strong for linear parabolic partial differential inequalities. We demonstrate, by careful construction specific function, that condition on coefficient zeroth-order term inequality cannot be relaxed to corresponding principle. addition, demonstrate results (often referred as boundary point lemmas) which conclude positivity outward directional derivatives nontrivial solutions inequalities at certain points where maxima is obtained under same