David Hruška (Univ. Leipzig): Regularity of saddle points in a model for ferrofluids
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.
Meeting ID: 962 1709 1997