[AN] Floris Roodenburg: Functional calculus for the Laplacian on weighted Sobolev spaces

17 September 2024 16:00 till 17:00 - Location: EEMCS Lecture Hall Chip | Add to my calendar

In this talk, we will consider the Laplace operator with Dirichlet and Neumann boundary conditions on the half-space and on bounded C1-domains. We study this operator on Sobolev spaces with power weights measuring the distance to the boundary. These weights play an important role in the study of (stochastic) partial differential equations on domains. It is found that the Laplace operator on weighted Sobolev spaces admits a bounded holomorphic functional calculus. As a consequence, we derive new maximal regularity results for the heat equation on weighted Sobolev spaces. In case of the half-space we additionally study the Dirichlet and Neumann heat semigroup and we show that this semigroup, in contrast to the Lp-case, has polynomial growth. This is joint work with Nick Lindemulder, Emiel Lorist and Mark Veraar.