We prove estimates for certain square functions of solutions to divergence form linear parabolic equations. The estimates are related to singularity and mutual absolute continuity of caloric measure with respect to surface measure of non-cylindrical domains. The square functions and the results included here are adapted from works on elliptic equations.
"Parabolic Square Functions and Caloric Measure." Commun. Math. Anal. 13 (1) 64 - 85, 2012.