Thesis defence C. Gallarati: equations
location: Aulam TU Delft
Maximal regularity for parabolic equations with measurable dependence on time and applications. Promotor: Prof.dr. J.M.A.M. van Neerven (EWI).
The subject of this thesis is the study of maximal Lp-regularity of the Cauchy problem
u0(t) + A(t)u(t) = f(t), t ∈ (0,T),
(1) u(0) = x.
We assume (A(t))t∈(0,T) to be a family of closed operators on a Banach space X0, with constant domain D(A(t)) = X1 for every t ∈ (0,T). Maximal Lp-regularity means that for all f ∈ Lp(0,T;X0), the solution of the evolution problem (1) is such that u0,Au are both in Lp(0,T;X0).
In the first part of the thesis, we introduce a new operator-theoretic approach to maximal Lp-regularity in the case the dependence on time is just measurable. The abstract method is then applied to concrete parabolic PDEs: we show that an elliptic operator of even order, with coefficients measurable in the time variable and continuous in the space variables, enjoys maximal Lp-regularity on Lq(Rd), for every p,q ∈ (1,∞). This gives an alternative approach to several PDE results in the literature, where only the cases p = q or q ≤ p were considered.
The last part of this thesis is devoted to the study of maximal Lp-regularity on) of an elliptic operator A with coefficients in the class of vanishing mean oscillation in the time and the space variables, and general boundary condition.
For access to theses by the PhD students you can have a look in TU Delft Repository, the digital storage of publications of TU Delft. Theses will be available within a few weeks after the actual thesis defence.