27 February 2024
16:00 till
17:00

### [AN] Moritz Egert: Bounded functional calculus and dynamical boundary conditions

We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a matter of fact, the elliptic operator and its semigroup act simultaneously in the interior and on (a part of) the boundary.

Over $L^2$ we have a m-sectorial operator by the form method, and we are interested in extrapolating the bounded $H^\infty$-calculus to $L^p$-spaces. We prove that this is possible if the coefficients satisfy an algebraic condition, called $p$-ellipticity, by adapting the heat flow/Bellman method of Carbonaro-DragiÄŤeviÄ‡ to our setting. A part of the talk will consist of a very gentle introduction to this technique that the speaker had to learn about from scratch before starting this project.

Joint work with Tim BĂ¶hnlein (TU Darmstadt) and Joachim Rehberg (WIAS Berlin).