Green's function, caloric measure and Fatou theorem for nondivergence parabolic equations in non cylindrical domains
Roberto Argiolas, Anna Piro Grimaldi · Forum Mathematicum · 2008
In this paper we are interested in studying parabolic operators in non-divergence form, in a class of time-varying domains. In particular, we establish the doubling properties for the Green's function and the normalized adjoint measure, and prove comparison theorems of Harnack type for adjoint solutions. Finally, we apply the above results to obtain Fatou theorem for nonnegative solutions. 2000 Mathematics Subject Classification: 35B65, 35C15, 35K20.