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 \({\Omega \subseteq \mathbb{R}^n}\). We obtain maximal regularity in \({L^2(\Omega)}\) 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 and Moritz Egert were partially supported by the ANR project “Harmonic Analysis at its Boundaries”, ANR-12-BS01-0013. Moritz Egert was supported by a public grant as part of the FMJH.
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Auscher, P., Egert, M. On non-autonomous maximal regularity for elliptic operators in divergence form. Arch. Math. 107, 271–284 (2016). https://doi.org/10.1007/s00013-016-0934-y
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DOI: https://doi.org/10.1007/s00013-016-0934-y