TY - JOUR
T1 - Maximum Principles for Second-order Parabolic Equations
AU - Antonio Vitolo 
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 - <p>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.</p>