Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations

Authors:	Matthias Hieber Sylvie Monniaux

Institution:	Mathematisches Institut I, Englerstr. 2, Universität Karlsruhe, D-76128 Karlsruhe, Germany ; Abteilung Mathematik V, Universität Ulm, D-89069 Ulm, Germany

Abstract:	In this paper, we show that a pseudo-differential operator associated to a symbol $a\in L^{\infty}(\mathbb{R}\times\mathbb{R},\mathcal{L}(H))$ ( being a Hilbert space) which admits a holomorphic extension to a suitable sector of $\mathbb{C}$ acts as a bounded operator on $L^{2}(\mathbb{R},H)$ . By showing that maximal $L^{p}$ -regularity for the non-autonomous parabolic equation is independent of $p\in (1,\infty)$ , we obtain as a consequence a maximal $L^{p}(0,T],H)$ -regularity result for solutions of the above equation.

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