Title: A new approach to maximal regularity for parabolic PDEs.
Maximal regularity can often be used to obtain a priori estimates which give global existence results. In this talk I will explain a new approach to maximal $L^p$-regularity for parabolic PDEs with time dependent generator $A(t)$. Here we do not assume any continuity properties of $A(t)$ as a function of time. We show that there is an abstract operator theoretic condition on A(t) which is sufficient to obtain maximal $L^p$-regularity. As an application I will obtain an optimal $L^p(L^q)$ regularity result in the case each $A(t)$ is a system of $2m$-th order elliptic differential operator on \R^d in non-divergence form. The main novelty in is that the coefficients are merely measurable in time and we allow the full range $1 This talk is based on joint work with Chiara Gallarati.
Location: KdVI Meeting Room (Science Park 105-107, F3.20)