Calculus of Variations
& Applications

Title: TBA

Abstract: TBA

Title: Non-trivial long-time dynamics in fluid-elastic interaction

Abstract:  Intuitively, the oscillations of an elastic structure immersed in a viscous liquid should be dampened over time. We set out to prove this by analysing the corresponding PDEs, but found more complex dynamics, depending on the structure's geometry. In the talk, I want to discuss these results and related methods and questions, associated also more generally to mixed parabolic-hyperbolic-type coupled systems. 

Title: Capillary surfaces: a model for nanowire growth and the capillary isoperimetric inequality outside convex sets

Abstract: In the first part of the talk, I will give an introductory overview of some recent results on a mathematical model for nanowire growth involving capillarity energy. I will discuss existence and non-existence of minimizers, as well as local minimality and regularity issues. In the second part, I will focus on the isoperimetric problem for capillary hypersurfaces outside arbitrary convex sets, with a general contact angle. I will show that the capillary energy of any such hypersurface is at least as large as that of a spherical cap enclosing the same volume and meeting a flat support at the same contact angle, and I will characterize the equality cases. This establishes the sharp isoperimetric inequality for capillary hypersurfaces outside convex sets at arbitrary contact angles, generalizing the well-known Choe–Ghomi–Ritoré inequality, which corresponds to orthogonal contact.