LP – SOLVABILITY OF THE DIRICHLET PROBLEM FOR THE HEAT OPERATOR IN NONCYLINDRICAL DOMAINS

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LP – SOLVABILITY OF THE DIRICHLET PROBLEM FOR THE HEAT OPERATOR IN NONCYLINDRICAL DOMAINS
L.I. Kurliykova
01.01.02
Yu.A. Alkhutov
доктор наук

We study the solvability 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 Lp-solvability condition and establish an Lp-estimate. The results are formulated in

terms of Muckenhoupt type conditions on the weight.

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