Mathematics > Analysis of PDEs
[Submitted on 24 Jan 2022 (v1), last revised 6 Oct 2023 (this version, v3)]
Title:$L^p$-estimates for the square root of elliptic systems with mixed boundary conditions II
View PDFAbstract:We show $L^p$ estimates for square roots of second order complex elliptic systems $L$ in divergence form on open sets in $\mathbb{R}^d$ subject to mixed boundary conditions. The underlying set is supposed to be locally uniform near the Neumann boundary part, and the Dirichlet boundary part is Ahlfors-David regular. The lower endpoint for the interval where such estimates are available is characterized by $p$-boundedness properties of the semigroup generated by $-L$, and the upper endpoint by extrapolation properties of the Lax-Milgram isomorphism. Also, we show that the extrapolation range is relatively open in $(1,\infty)$.
Submission history
From: Sebastian Bechtel [view email] [via CCSD proxy][v1] Mon, 24 Jan 2022 10:03:37 UTC (28 KB)
[v2] Mon, 24 Oct 2022 10:58:48 UTC (26 KB)
[v3] Fri, 6 Oct 2023 13:05:15 UTC (23 KB)
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