Zobrazeno 1 - 10
of 92
pro vyhledávání: '"Cinti, Eleonora"'
Autor:
Cinti, Eleonora, Prinari, Francesca
We show that, when $sp>N$, the sharp Hardy constant $\mathfrak{h}_{s,p}$ of the punctured space $\mathbb R^N\setminus\{0\}$ in the Sobolev-Slobodecki\u{\i} space provides an optimal lower bound for the Hardy constant $\mathfrak{h}_{s,p}(\Omega)$ of a
Externí odkaz:
http://arxiv.org/abs/2407.06568
We establish a regularity result for optimal sets of the isoperimetric problem with double density under mild ($\alpha$-)H\"older regularity assumptions on the density functions. Our main Theorem improves some previous results and allows to reach in
Externí odkaz:
http://arxiv.org/abs/2304.05867
Autor:
Cinti, Eleonora, Colasuonno, Francesca
We establish a priori $L^\infty$-estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion coefficien
Externí odkaz:
http://arxiv.org/abs/2211.08315
Autor:
Cinti, Eleonora <1982>
This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional s
Externí odkaz:
http://amsdottorato.unibo.it/3073/
We study stable solutions to the fractional Allen-Cahn equation \linebreak $(-\Delta)^{s/2} u = u-u^3$, $|u|<1$ in $\mathbb{R}^n$. For every $s\in (0,1)$ and dimension $n\geq 2$, we establish sharp energy estimates, density estimates, and the converg
Externí odkaz:
http://arxiv.org/abs/2111.06285
The aim of this work is to show a non-sharp quantitative stability version of the fractional isocapacitary inequality. In particular, we provide a lower bound for the isocapacitary deficit in terms of the Fraenkel asymmetry. In addition, we provide t
Externí odkaz:
http://arxiv.org/abs/2107.08257
We prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homogeneous weights. Inspired by the proof of such isoperimetric inequaliti
Externí odkaz:
http://arxiv.org/abs/2006.13867
Autor:
Cinti, Eleonora, Colasuonno, Francesca
Publikováno v:
J. Differential Equations 268 (2020), no. 5, 2246-2279
We establish existence of positive non-decreasing radial solutions for a nonlocal nonlinear Neumann problem both in the ball and in the annulus. The nonlinearity that we consider is rather general, allowing for supercritical growth (in the sense of S
Externí odkaz:
http://arxiv.org/abs/1904.02635
Publikováno v:
J. Funct. Anal., 279-3 (2020), 1-49
We prove a quantitative version of the Faber-Krahn inequality for the first eigenvalue of the fractional Dirichlet-Laplacian of order s. This is done by using the so-called Caffarelli-Silvestre extension and adapting to the nonlocal setting a trick b
Externí odkaz:
http://arxiv.org/abs/1901.10845
Publikováno v:
Analysis & PDE 13 (2020) 2149-2171
We consider the volume preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long time asymptotics approach ro
Externí odkaz:
http://arxiv.org/abs/1811.08651