Maximum Principles for Second-order Parabolic Equations

Abstract

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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 Cabr\u00e9, 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\fnite cylindrical and non-cylindrical domains.<\/p>"