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arXiv · 1611.09064

Non-Autonomous Maximal $L^p$-Regularity under Fractional Sobolev Regularity in Time

Stephan Fackler
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Abstract

We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common H\"older assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In particular, on $L^q(\Omega)$ we obtain maximal $L^p$-regularity for $p \ge 2$ and elliptic operators in divergence form with uniform $VMO$-modulus in space and $W^{\alpha,p}$-regularity for $\alpha > \frac{1}{2}$ in time.

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Stephan Fackler. 2016-11-28. Non-Autonomous Maximal $L^p$-Regularity under Fractional Sobolev Regularity in Time. https://doi.org/10.2140/apde.2018.11.1143

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