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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

Chiara Gallarati (Delft University of Technology)

Maximal regularity for non-autonomous parabolic equations

Maximal regularity is a useful tool 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 $A(t)$. The novelty is that I merely assume a measurable dependence on time. I will first 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 2m-th order elliptic differential operator on $\mathbb{R}^d$ in non-divergence form, for every $p,q\in (1,\infty)$. This is a joint work with Mark Veraar (TU Delft).