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 | References | Similar Articles | Additional Information

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 with time dependent boundary, map into an appropriate homogeneous Sobolev space. The simplification is achieved by treating directly only the case , but in a weighted setting.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1137222-7

Article copyright:
© Copyright 1993
American Mathematical Society