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An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains
PDE and Applied Math Seminar| Speaker: | Liding Yao, University of Wisconsin |
| Location: | ZOOM https://ucdavis.zoom.us/j/91871335293?pwd=SCs2dlgxYU0yQ05IaWk4c05Xc25SUT09 |
| Start time: | Fri, Nov 19 2021, 10:00AM |
Given a bounded Lipschitz domain $\Omega\subset\mathbb R^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. In this paper we introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative smoothing estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.