# Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains

Research output: Preprint/documentation/report â€º Preprint

## Contributors

## Abstract

We investigate the boundary trace operators that naturally correspond to $\mathrm{H}(\operatorname{curl},\Omega)$, namely the tangential and twisted tangential trace, where $\Omega \subseteq \mathbb{R}^{3}$. In particular we regard partial tangential traces, i.e., we look only on a subset $\Gamma$ of the boundary $\partial\Omega$. We assume both $\Omega$ and $\Gamma$ to be strongly Lipschitz. We define the space of all $\mathrm{H}(\operatorname{curl},\Omega)$ fields that possess a $\mathrm{L}^{2}$ tangential trace in a weak sense and show that the set of all smooth fields is dense in that space, which is a generalization of \cite{BeBeCoDa97}. This is especially important for Maxwell's equation with mixed boundary condition as we answer the open problem by Weiss and Staffans in \cite[Sec.~5]{WeSt13} for strongly Lipschitz pairs.

## Details

Original language | Undefined |
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Publication status | Published - 26 Sept 2023 |

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## External IDs

ORCID | /0000-0003-4155-7297/work/145698483 |
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## Keywords

### Keywords

- math.FA, math.AP, 46E35, 35Q61