Speaker
Description
In this talk, we present new insights into the regularity of elliptic systems within certain three-dimensional polyhedral domains under mixed boundary conditions.
Our approach begins by analyzing geometric model problems, focusing on a \linebreak two-dimensional angle that naturally extends to edges in three dimensions.
Utilizing algebraic properties of the elliptic system, we construct a solution basis for the model problem in the absence of boundary conditions. When mixed boundary conditions are introduced, the regularity problem is reduced to the analysis of an associated matrix equation. By further employing numerical range properties and accretive operator theory, we derive regularity results for the solutions.
This framework also covers other boundary conditions and might be adaptable to further scenarios like higher-order elliptic equations or three-dimensional problems posed within conical geometries. The outcome of this theory can also be applied to establish new regularity results for problems in linear elasticity.
