GS Advanced Topics in PDE: Boundary determination in anisotropic elasticity

by Dr Hjørdis Schlüter (Helsinki)

Friday Oct 17, 2025, 2:00 PM → 4:00 PM Europe/Berlin

This is joint work with Joonas Ilmavirta, Mikko Salo and Daniel Windisch. I will talk about the elastic wave equation that models waves that propagate through elastic media. We are particularly interested in materials that are highly anisotropic and aim at recovering the density of mass and the so-called stiffness tensor, that capture the elasticity of the material, from exterior measurements. The exterior measurement that we consider is the Dirichlet-to-Neumann map. I will talk about a recent result, where we for generic stiffness tensor fields are able to determine the normalized stiffness tensor (where we are not able to distinguish between density and stiffness tensor) at the boundary of the medium. For this result we need a construction of special solutions and employ tools from algebraic geometry.