Non-autonomous Lq(Lp) maximal regularity for complex systems under mixed regularity in space and time

Publikationstyp
Preprint
Date Issued
2022-08
Sprache
English
Author(s)
Bechtel, Sebastian  
Gabel, Fabian Nuraddin Alexander 
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/13412
Citation
arXiv: 2208.02527 (2022)
Publisher DOI
10.48550/arXiv.2208.02527
Publisher Link
https://hal.archives-ouvertes.fr/hal-03745208v1
ArXiv ID
2208.02527
Peer Reviewed
false
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.
Subjects
Lions problem
second-order elliptic systems
commutator estimates
non-autonomous maximal regularity
DDC Class
510: Mathematik