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arXiv · 1705.11054

Complex interpolation with Dirichlet boundary conditions on the half line

Nick Lindemulder·Martin Meyries·Mark Veraar
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Abstract

We prove results on complex interpolation of vector-valued Sobolev spaces over the half-line with Dirichlet boundary condition. Motivated by applications in evolution equations, the results are presented for Banach space-valued Sobolev spaces with a power weight. The proof is based on recent results on pointwise multipliers in Bessel potential spaces, for which we present a new and simpler proof as well. We apply the results to characterize the fractional domain spaces of the first derivative operator on the half line.

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Nick Lindemulder, Martin Meyries, Mark Veraar. 2017-05-31. Complex interpolation with Dirichlet boundary conditions on the half line. https://arxiv.org/abs/1705.11054

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