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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…
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…
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…
Regularity near the fixed boundary for transmission systems
Alessio Figalli, Somayeh Khademloo, Sunghan Kim +1
Given with , open, and , we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)χ_D)\nabla u\big) =…
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…