Zobrazeno 1 - 10
of 455
pro vyhledávání: '"Figalli Alessio"'
Autor:
Figalli Alessio, Jhaveri Yash
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 365-417 (2023)
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 when the support of the target measure is an arbitrary convex domain an
Externí odkaz:
https://doaj.org/article/55c2c27b63174d36af04c0bb9052d637
Autor:
Figalli, Alessio, Ramos, João P. G.
We consider the problem of stability for the Pr\'ekopa-Leindler inequality. Exploiting properties of the transport map between radially decreasing functions and a suitable functional version of the trace inequality, we obtain a uniform stability expo
Externí odkaz:
http://arxiv.org/abs/2410.01122
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 diverse structure that includes singularities similar to harmonic maps, bra
Externí odkaz:
http://arxiv.org/abs/2407.21128
The Brunn-Minkowski inequality, applicable to bounded measurable sets $A$ and $B$ in $\mathbb{R}^d$, states that $|A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}$. Equality is achieved if and only if $A$ and $B$ are convex and homothetic sets in $\mathbb{R}^d$.
Externí odkaz:
http://arxiv.org/abs/2407.10932
Autor:
Figalli, Alessio, Zhang, Yi Ru-Ya
The classical Serrin's overdetermined theorem states that a $C^2$ bounded domain, which admits a function with constant Laplacian that satisfies both constant Dirichlet and Neumann boundary conditions, must necessarily be a ball. While extensions of
Externí odkaz:
http://arxiv.org/abs/2407.02293
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 probability densities in $\R^d$. Our focus is on a broader category of densities
Externí odkaz:
http://arxiv.org/abs/2404.05456
Given $\Omega\subset \mathbb{R}^n$ with $n\geq 2$, $D\subset \Omega$ open, and $u:\Omega \to \mathbb{R}^m$, we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)\chi_D)\nabla u\big) = 0 \quad \text{in $\Omega\cap B_1$,} $$ for some un
Externí odkaz:
http://arxiv.org/abs/2403.04406
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 Sobolev inequality obtained by the authors in [24]. The stability for the
Externí odkaz:
http://arxiv.org/abs/2402.08527
In this manuscript, we delve into the study of maps $u\in W^{1,2}(\Omega;\overline M)$ that minimize the Alt-Caffarelli energy functional $$ \int_\Omega (|Du|^2 + q^2 \chi_{u^{-1}(M)})\,dx, $$ under the condition that the image $u(\Omega)$ is confine
Externí odkaz:
http://arxiv.org/abs/2311.03006
The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in $\mathbb{R}^n$, we have $|A+B|^{1/n} \geq |A|^{1/n}+|B|^{1/n}$. Also, equality holds if and only if $A$ and $B$ are convex and homothetic sets in $\mathbb{R}^d$. Th
Externí odkaz:
http://arxiv.org/abs/2310.20643