Higher dimensional scattering theory and integral representation formulas

Dorina Mitrea (Baylor U, Waco)

Nov 09. 2022, 09:00 — 09:45

In this talk I will answer the following basic question:

What are the optimal assumptions, of geometric and analytic nature, which
guarantee that a null-solution $u$ of the Helmholtz operator $\Delta+k^2$
in an exterior domain $\Omega$ can be represented in terms of layer potentials
naturally associated with the said Helmholtz operator and given domain?

This work, at the interface between Geometric Measure Theory, Harmonic Analysis,
Scattering Theory, and Clifford Analysis, generalizes and unifies classical results
of Sommerfeld, Weyl, M\"uller, and Calder\'on. I will also explore similar issues in relation
to the Stokes system of hydrodynamics.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory of Differential Operators in Quantum Theory (Workshop)
Jussi Behrndt (TU Graz)
Fritz Gesztesy (Baylor U, Waco)
Ari Laptev (Imperial College London)
Christiane Tretter (U Bern)