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Proceedings of the American Mathematical Society

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A note on weighted Sobolev spaces, and regularity of commutators and layer potentials associated to the heat equation


Author: Steve Hofmann
Journal: Proc. Amer. Math. Soc. 118 (1993), 1087-1096
MSC: Primary 42A50; Secondary 35K05, 42B25, 47N20
DOI: https://doi.org/10.1090/S0002-9939-1993-1137222-7
MathSciNet review: 1137222
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Abstract: We give a simplified proof of recent regularity results of Lewis and Murray, namely, that certain commutators, and the boundary single layer potential for the heat equation in domains in $ {\mathbb{R}^2}$ with time dependent boundary, map $ {L^p}$ into an appropriate homogeneous Sobolev space. The simplification is achieved by treating directly only the case $ p = 2$, but in a weighted setting.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1137222-7
Article copyright: © Copyright 1993 American Mathematical Society