Verlagslink: https://hal.archives-ouvertes.fr/hal-03745208v1
arXiv ID: 2208.02527
Titel: Non-autonomous Lq(Lp) maximal regularity for complex systems under mixed regularity in space and time
Sprache: Englisch
Autor/Autorin: Bechtel, Sebastian 
Gabel, Fabian Nuraddin Alexander  
Schlagwörter: Lions problem; second-order elliptic systems; commutator estimates; non-autonomous maximal regularity
Erscheinungs­datum: Aug-2022
Zusammenfassung (englisch): 
We 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.
URI: http://hdl.handle.net/11420/13412
Institut: Mathematik E-10 
Dokumenttyp: Vorabdruck (Preprint)
Peer Reviewed: Nein
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