Abstract
We consider the maximal regularity problem for non-autonomous evolution equations
Each operator A(t) is associated with a sesquilinear form a(t) on a Hilbert space H. We assume that these forms all have the same domain V. It is proved in Haak and Ouhabaz (Math Ann, doi:10.1007/s00208-015-1199-7, 2015) that if the forms have some regularity with respect to t (e.g., piecewise α-Hölder continuous for some α > ½) then the above problem has maximal L p -regularity for all u 0 in the real-interpolation space \((H, \fancyscript{D}(A(0)))_{1-{1}/{p},p}\). In this paper we prove that the regularity required there can be improved for a class of sesquilinear forms. The forms considered here are such that the difference a(t;.,.) − a(s;.,.) is continuous on a larger space than the common domain V. We give three examples which illustrate our results.
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The research of the author was partially supported by the ANR project HAB, ANR-12-BS01-0013-02.
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Ouhabaz, E.M. Maximal regularity for non-autonomous evolution equations governed by forms having less regularity. Arch. Math. 105, 79–91 (2015). https://doi.org/10.1007/s00013-015-0783-0
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DOI: https://doi.org/10.1007/s00013-015-0783-0