DIVERGENCE FORM PARABOLIC EQUATIONS ON TIME-DEPENDENT QUASICONVEX DOMAINS

摘要

In this paper, we show the regularity of divergence form parabolic equations on time-dependent quasiconvex domains. The objective is to study the optimal parabolic boundary condition for the Lp estimates. The time-dependent quasiconvex domain is a generalization of the time-dependent Reifenberg flat domain, and assesses some properties analog to the convex domain. As to the a priori estimates near the boundary, we will apply the maximal function technique, Vitali covering lemma and the compactness method.