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

Abstract

We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common Hölder 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.

19 pages

References in corpus (3)

• Elliptic equations in divergence form with partially BMO coefficients
• J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms
• Evolution families and maximal regularity for systems of parabolic equations

Cited by in corpus (5)

• Lp-estimates for the square root of elliptic systems with mixed boundary conditions
• The Kato Square Root Problem on locally uniform domains
• Counterexamples to maximal regularity for operators in divergence form
• Weighted non-autonomous $L^q(L^p)$ maximal regularity for complex systems
• J. L. Lions' Problem on Maximal Regularity