Solvability of the dirichlet problem for the heat equation in noncylindrical domains with isolated characteristic points at the boundary

We study the solvabitlity of the Dirichlet problem for the heat operator in weighted Sobolev [L.sub.p]-spaces in noncylindrical paraboloid type domains with isolated characteristic points at the boundary. For any p > 1 we find a necessary and sufficient [L.sub.p]-solvability condition and establish an [L.sub.p]-estimate. The results are formulated in terms of Muckenhoupt type conditions on the weight. Bibliography: 10 titles.