Non-autonomous right and left multiplicative perturbations and maximal regularity

Mahdi Achache, El Maati Ouhabaz
2018 Studia Mathematica  
We consider the problem of maximal regularity for non-autonomous Cauchy problems In both cases, the time dependent operators A(t) are associated with a family of sesquilinear forms and the multiplicative left or right perturbations B(t) as well as the additive perturbation P (t) are families of bounded operators on the considered Hilbert space. We prove maximal L p -regularity results and other regularity properties for the solutions of the previous problems under minimal regularity assumptions
more » ... ularity assumptions on the forms and perturbations. keywords: Maximal regularity, non-autonomous evolution equations, multiplicative and additive perturbations. Mathematics Subject Classification (2010): 35K90, 35K45, 47D06.
doi:10.4064/sm8721-6-2017 fatcat:cvvcnpodf5bu5oo3td3crhaqbu