Friday, April 20, 2018 - 14:15 in V4-119
Singular SPDEs in domains with boundaries
A talk in the Bielefeld Stochastic Afternoon series by
Máté Gerencsér from IST Austria
| Abstract: |
We discuss how the presence of boundaries and boundary conditions such as Dirichlet or Neumann effect the theory of
regularity structures.
While a significant part of the theory can be carried through using appropriately weighted modifications of the spaces of
modelled distributions, some new difficulties arise due to an important threshold -2 (the codimension of the temporal boundary) being raised to -1 (the codimension of the spatial boundary), which forces the reconstruction operator to be non-unique in a number of relevant situations.
As a consequence, in certain equations a "boundary renormalisation" takes place.
Some examples for this effect, in the case of the KPZ, PAM, or $\Phi^4_3$ equations, will be outlined.
Joint work with Martin Hairer.
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