MAXIMUM PRINCIPLES FOR SECOND-ORDER PARABOLIC EQUATIONS
AntonioVitolo · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2004
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 Cabre, 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 infinite cylindrical and non-cylindrical domains.