Abstract
We study the invertibility of $\lambda I+K$ in $L^p(\partial\Omega\times\mathbf{R})$, for $p$ near $2$ and $\lambda\in\mathbf{R}$, $|\lambda|\geq\sfrac12$, where $K$ is the caloric double layer potential operator and $\Omega$ is a Lipschitz domain. Applications to transmission boundary value problems are also presented.
Citation
Steve Hofmann. John Lewis. Marius Mitrea. "Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains." Illinois J. Math. 47 (4) 1345 - 1361, Winter 2003. https://doi.org/10.1215/ijm/1258138108
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