7 papers · 1 filter
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 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…
Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation
Alessio Figalli, Peter van Hintum, Marius Tiba
The Brunn-Minkowski inequality, applicable to bounded measurable sets and in , states that . Equality is achieved if and…
A short review on Improvements and stability for some interpolation inequalities
Jean Dolbeault, Maria J. Esteban, Alessio Figalli +2
In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sob…
On Optimal Transport Maps Between 1 /d-Concave Densities
Guillaume Carlier, Alessio Figalli, Filippo Santambrogio
In this paper, we extend the scope of Caffarelli's contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probabilit…