4 papers · 2 filters
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.…
On the existence of degenerate solutions of the two-dimensional -system
André Guerra, Xavier Lamy, Konstantinos Zemas
We consider entire solutions of the -system which we refer to as bubbles. Surprisingly, and contrary to conjectu…
Constraint maps with free boundaries: the Bernoulli case
Alessio Figalli, André Guerra, Sunghan Kim +1
In this manuscript, we delve into the study of maps that minimize the Alt-Caffarelli energy functional $$ \int_Ω(|Du|^2 + q^2 Ï_{u^{-1}(M)})\,dx, $…
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…