Analysis Seminar: Multilayer Potentials for $\Delta^3$ in Infinitesimally Flat Ahlfors Regular Domains

Abstract: Much remains to be understood and structurally addressed in the employment of the layer potential method for the treatment of boundary value problems for higher-order elliptic operators. In this talk I will discuss boundary-to-boundary double multilayers associated with $\Delta^3$ in UR domains in the Euclidean space. The focus is on identifying a double multilayer that is sensitive to the flatness of the domain under consideration, thus opening the door for the employment of Fredholm theory in the study of the Dirichlet problem for $\Delta^3$ in bounded infinitesimally flat Ahlfors Regular domains.

This is an ongoing work with Dorina Mitrea (Baylor University), Irina Mitrea (Temple University), and Marius Mitrea (Baylor University).

Host: Brett Wick