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arXiv · 1602.08306

On non-autonomous maximal regularity for elliptic operators in divergence form

Pascal Auscher·Moritz Egert
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Abstract

We consider the Cauchy problem for non-autonomous forms inducing elliptic operators in divergence form with Dirichlet, Neumann, or mixed boundary conditions on an open subset $Ω$ $\subseteq$ R n. We obtain maximal regularity in L 2 ($Ω$) if the coefficients are bounded, uniformly elliptic, and satisfy a scale invariant bound on their fractional time-derivative of order one-half. Previous results even for such forms required control on a time-derivative of order larger than one-half.

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Pascal Auscher, Moritz Egert. 2019-12-05. On non-autonomous maximal regularity for elliptic operators in divergence form. https://arxiv.org/abs/1602.08306

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