A. Figalli

activity

20062026

most citedThe power of quantum neural networks

1k citations · 1.7k across the 85 of their papers we have counts for

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Showing 2023Show all

7 papers · 1 filter

math.AP2023

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 $u \in W^{1, 2} (Ω; M)$ that minimize the Alt-Caffarelli energy functional $\int_{Ω} (∣ D u ∣^{2} + q^{2} χ_{u^{- 1} (M)}) d x,$ u…

math.AP2023

Sharp quantitative stability of the Brunn-Minkowski inequality

Alessio Figalli, Peter van Hintum, Marius Tiba

The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in $R^{n}$ , we have $∣ A + B ∣^{1/ n} \geq ∣ A ∣^{1/ n} + ∣ B ∣^{1/ n}$ . Also, equality holds if and on…

math.AP2023★ 1 cited

The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains

Matteo Bonforte, Alessio Figalli

The Fast Diffusion Equation (FDE) $u_{t} = Δ u^{m}$ , with $m \in (0, 1)$ , is an important model for singular nonlinear (density dependent) diffusive phenomena. Here, we focus on the Cauchy…

math.OC2023

Strong stability of convexity with respect to the perimeter

Alessio Figalli, Yi Ru-Ya Zhang

Let $E \subset R^{n}$ , $n \geq 2$ , be a set of finite perimeter with $∣ E ∣ = ∣ B ∣$ , where $B$ denotes the unit ball. When $n = 2$ , since convexification decreases perimeter (in the cl…

math.AP2023★ 2 cited

Regularity theory for nonlocal obstacle problems with critical and subcritical scaling

Alessio Figalli, Xavier Ros-Oton, Joaquim Serra

Despite significant recent advances in the regularity theory for obstacle problems with integro-differential operators, some fundamental questions remained open. On the one hand, t…

math.AP2023

Regularity Properties of Monotone Measure-preserving Maps

Alessio Figalli, Yash Jhaveri

In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case w…