Bechtel, SebastianSebastianBechtelGabel, Fabian Nuraddin AlexanderFabian Nuraddin AlexanderGabel2022-08-082022-08-082022-08arXiv: 2208.02527 (2022)http://hdl.handle.net/11420/13412We show non-autonomous Lq(Lp) maximal regularity for families of complex second-order systems in divergence form under a mixed Hölder regularity condition in space and time. To be more precise, we let p,q∈(1,∞) and we consider coefficient functions in Cβ+ε with values in Cα+ε subject to the parabolic relation 2β+α=1. To this end, we provide a weak (p,q)-solution theory with uniform constants and establish a priori higher spatial regularity. Furthermore, we show p-bounds for semigroups and square roots generated by complex elliptic systems under a minimal regularity assumption for the coefficients.enLions problemsecond-order elliptic systemscommutator estimatesnon-autonomous maximal regularityMathematikPreprint10.48550/arXiv.2208.02527https://hal.archives-ouvertes.fr/hal-03745208v12208.02527Preprint