THE DIRICHLET PROBLEM FOR 2ND-ORDER PARABOLIC OPERATORS

We develop the harmonic analysis approach for general second order par abolic operators in divergence form (i.e., allowing for time dependent coefficients) in the setting of a class of time-varying domains. More precisely we prove doubling properties of the associated caloric meas ure, we define and study the kernel function and prove the relevant es timates for the non-tangential maximal function and the area integral. All these tools are considered in order to prove some perturbation re sults for the Dirichlet problem with data on the lateral boundary of o ur time-varying cylinder.