4 papers · 1 filter
Constancy of the index for gradient mappings
André Guerra, Riccardo Tione
We show that if the Hessian of a function has uniformly positive determinant almost everywhere then its index is locally constant, as conjectured by Šverák in 1992. We de…
Constraint maps and free boundaries
Alessio Figalli, André Guerra, Sunghan Kim +1
In this short expository note, we present a selection of classic and recent ideas in free boundary theory, with a focus on the vectorial case, referred to here as constraint maps.…
Constraint maps: singularities vs free boundaries
Alessio Figalli, André Guerra, Sunghan Kim +1
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diver…
Regularity and compactness for critical points of degenerate polyconvex energies
André Guerra, Riccardo Tione
We study Lipschitz critical points of the energy in two dimensions, where is a strictly convex function. We prove that the Jacobian of any Lipschitz…