L_p-SOLVABILITY OF THE DIRICHLET PROBLEM FOR THE HEAT EQUATION IN NONCYLINDRICAL DOMAINS WITH ISOLATED CHARACTERISTIC POINTS AT THE BOUNDARY

摘要

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