A note on weighted Sobolev spaces, and regularity of commutators and layer potentials associated to the heat equation
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- Proc. Amer. Math. Soc. 118 (1993), 1087-1096 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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