3 papers
math.AP2024
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.…
math.AP2024
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…
math.AP2024
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…