Localization of trace norms in two and three dimensions
Silvia Bertoluzza · arXiv (Cornell University) · 2023
We extend a localization result for the $H^{1/2}$ norm by B. Faermann to a wider class of subspaces of $H^{1/2}(Γ)$, and we prove an analogous result for the $H^{-1/2}(Γ)$ norm, $Γ$ being the boundary of a bounded polytopal domain $Ω$ in $\mathbb{R}^n$, $n=2,3$. As a corollary, we obtain equivalent, better localized, norms for both $H^{1/2}(Γ)$ and $H^{-1/2}(Γ)$, which can be exploited, for instance, in the design of preconditioners or of stabilized methods.