arXiv 1602.083062016-02math.FAmath.AP

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

Pascal Auscher, Moritz Egert

备注：: All results unchanged. We corrected a wrong statement in the introduction of the published version concerning operator norms and uniform bounds for the coefficient matrix that was only used to illustrate the relation with earlier work. For these statements only, coefficients should be real and symmetric
发表信息：: Archiv der Mathematik, Springer Verlag, 2016, 107 (3), pp.271-284

英文摘要：

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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英文摘要：

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