%0 Journal Article %T A centennial of the Zaremba--Hopf--Oleinik Lemma %A Alexander I. Nazarov %J Mathematics %D 2010 %I arXiv %X We discuss the problem how "bad" may be lower-order coefficients in elliptic and parabolic second order equations to ensure the Hopf--Oleinik Lemma for solutions to hold true. We also touch the gradient estimates for solutions at the boundary. %U http://arxiv.org/abs/1101.0164v2