A Direct Method for Time-Periodic L^p Estimates
- Jonas Sauer (MPI MiS, Leipzig)
Inbetween elliptic PDEs, which do not depend on time (think of the Poisson equation), and honest parabolic PDEs, which do depend on time and are started at a given initial value (think of the heat equation), there are time-periodic parabolic PDEs: On the one hand, time-independent solutions to the elliptic PDE are also trivially time-periodic, which gives periodic problems an elliptic touch, on the other hand solutions to the initial value problem which are not constant in time might very well be periodic.
I want to advocate for time-periodic problems not being the little sister of either elliptic or parabolic problems, but being a connector between the two and a class of its own right, by introducing a direct method for showing a priori $L^p$ estimates for time-periodic, linear, partial differential equations. The method is generic and can be applied to a wide range of problems. In the talk, I intend to demonstrate it on the heat equation and on boundary value problems of Agmon-Douglas-Nirenberg type.
The talk is based on joint works with Yasunori Maekawa and Mads Kyed.