Exterior value problems for integro-differential operators
A talk in the Nonlocal Equations: Analysis and Numerics series by
Florian Grube from Bielefeld
| Abstract: | In this talk, we discuss two results on exterior value problems for integrodifferential operators. In the first part, we study a variational setup to
Dirichlet problems involving nonlocal operators like the fractional p-Laplacian
in bounded domains. In particular, we answer the question for which exterior data weak solutions in an appropriate Sobolev-like function space exist.
This entails appropriate trace and extension theorems. The fractional p-Laplacian converges to a classical differential operator as the order of differentiation increases to two. This phenomenon will be of particular interest
to us. In the second part of the talk, we discuss existence, uniqueness,
and regularity of distributional solutions to linear exterior-value problems
involving 2s-stable operators with square integrable exterior data. As we
will have seen in the first part of the talk, these data are too irregular for the
corresponding Dirichlet problem to be solved with variational methods. Within the CRC this talk is associated to the project(s): A7 |