TY - JOUR T1 - Maximum Principles for Second-order Parabolic Equations JO - Journal of Partial Differential Equations VL - 4 SP - 289 EP - 302 PY - 2004 DA - 2004/11 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5394.html KW - Maximum principle KW - ABP estimate KW - parabolic equations AB -

This paper is the parabolic counterpart of previous ones about elliptic operators in unbounded domains. Maximum principles for second-order linear parabolic equations are established showing a variant of the ABP-Krylov-Tso estimate, based on the extension of a technique introduced by Cabré, which in turn makes use of a lower bound for super-solutions due to Krylov and Safonov. The results imply the uniqueness for the Cauchy-Dirichlet problem in a large class of in nite cylindrical and non-cylindrical domains.