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- W4287644299 abstract "We study the dependence of the continuity constants for the regularized Poincar'e and Bogovskiu{i} integral operators acting on differential forms defined on a domain $Omega$ of $mathbb{R}^n$. We, in particular, study the dependence of such constants on certain geometric characteristics of the domain when these operators are considered as mappings from (a subset of) $L^2(Omega,Lambda^ell)$ to $H^1(Omega,Lambda^{ell-1})$, $ell in {1, ldots, n}$. For domains $Omega$ that are star shaped with respect to a ball $B$ we study the dependence of the constants on the ratio $diam(Omega)/diam(B)$. A program on how to develop estimates for higher order Sobolev norms is presented. The results are extended to certain classes of unions of star shaped domains." @default.
- W4287644299 created "2022-07-25" @default.
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- W4287644299 date "2020-10-08" @default.
- W4287644299 modified "2023-10-17" @default.
- W4287644299 title "Estimation of the continuity constants for Bogovskiu{i} and regularized Poincar'e integral operators" @default.
- W4287644299 doi "https://doi.org/10.48550/arxiv.2010.04105" @default.
- W4287644299 hasPublicationYear "2020" @default.
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