David Hruška (Univ. Leipzig): Regularity of saddle points in a model for ferrofluids

Abstract:
We will discuss regularity results for saddle points for a class of free  boundary problems motivated by a variational model introduced in the  paper Parini, E., Stylianou, A.: A free boundary approach to the Rosensweig instability of ferrofluids.  Namely, we are concerned with saddle points to functionals of the type
J(u,E) = Per(E) + G(E) - J1(u,E)
where G are geometric quantities of  lower order and J1 is a (nonlinear) Dirichlet-type energy strictly convex in ∇u but non-smooth across ∂E. After a brief  discussion on the physical background we sketch how to apply the  powerful methods originally developed by De Giorgi and Almgren for  regularity of minimal surfaces (and later generalized e.g. for  free boundary problems arising from electrostatics) to our functional, which  is non-linear and of saddle nature.
This is a joint work with Jonas Hirsch from Leipzig University.

Zoom Link:
uni-kassel.zoom.us/j/96217091997

Meeting ID: 962 1709 1997
Passcode: cauchy