Séminaire Analyse Harmonique
Square function estimates for a heat flow with dynamic boundary conditions
01
Oct. 2024
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Intervenant : Moritz Egert
Institution : TU Darmstadt
Heure : 14h00 - 15h00
Lieu : Salle 2L8

We consider elliptic divergence form operators $L$ in open subsets of Euclidean space. We let the Dirichlet energy induce a heat flow simultaneously in the set and on the boundary. This corresponds to dynamic boundary conditions in the parabolic problem. We will explain how to prove $L^p$ square function estimates for the corresponding heat semigroup $\exp(tL)$. The main obstacle is that different parts of the underlying geometric domain (namely, interior and boundary) have different scaling dimensions.

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