Zobrazeno 1 - 10
of 231
pro vyhledávání: '"Fragalà, Ilaria"'
For any $p \in ( 1, +\infty)$, we give a new inequality for the first nontrivial Neumann eigenvalue $\mu _ p (\Omega, \varphi)$ of the $p$-Laplacian on a convex domain $\Omega \subset \mathbb{R}^N$ with a power-concave weight $\varphi$. Our result im
Externí odkaz:
http://arxiv.org/abs/2407.20373
The fundamental gap conjecture proved by Andrews and Clutterbuck in 2011 provides the sharp lower bound for the difference between the first two Dirichlet Laplacian eigenvalues in terms of the diameter of a convex set in $\mathbb{R}^N$. The question
Externí odkaz:
http://arxiv.org/abs/2407.01341
We prove the existence of periodic tessellations of $\mathbb{R}^N$ minimizing a general nonlocal perimeter functional, defined as the interaction between a set and its complement through a nonnegative kernel, which we assume to be either integrable a
Externí odkaz:
http://arxiv.org/abs/2310.01054
Autor:
Crasta, Graziano, Fragalà, Ilaria
Publikováno v:
Arch. Rational Mech. Anal. 248:48 (2024)
We introduce an evolution model \`a la Firey for a convex stone which tumbles on a beach and undertakes an erosion process depending on some variational energy, such as torsional rigidity, principal Dirichlet Laplacian eigenvalue, or Newtonian capaci
Externí odkaz:
http://arxiv.org/abs/2303.11764
Given a non-increasing and radially symmetric kernel in $L ^ 1 _{\rm loc} (\Bbb{R} ^ 2 ; \Bbb{R}_+)$, we investigate counterparts of the classical Hardy-Littlewood and Riesz inequalities when the class of admissible domains is the family of polygons
Externí odkaz:
http://arxiv.org/abs/2302.11677
Autor:
Crasta, Graziano, Fragalà, Ilaria
We introduce a new operation between nonnegative integrable functions on $\mathbb{R} ^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature of this ope
Externí odkaz:
http://arxiv.org/abs/2204.11521
Autor:
Bucur, Dorin, Fragalà, Ilaria
For a general radially symmetric, non-increasing, non-negative kernel $h\in L ^ 1 _{loc} ( R ^ d)$, we study the rigidity of measurable sets in $R ^ d$ with constant nonlocal $h$-mean curvature. Under a suitable "improved integrability" assumption on
Externí odkaz:
http://arxiv.org/abs/2202.03180
Autor:
Bucur, Dorin, Fragalà, Ilaria
Let $\Omega \subset \mathbb{R}^d$ be a set with finite Lebesgue measure such that, for a fixed radius $r>0$, the Lebesgue measure of $\Omega \cap B_r (x)$ is equal to a positive constant when $x$ varies in the essential boundary of $\Omega$. We prove
Externí odkaz:
http://arxiv.org/abs/2102.12389
We introduce a new method for constructing solenoidal extensions of fairly general boundary data in (2d or 3d) cubes that contain an obstacle. This method allows us to provide explicit bounds for the Dirichlet norm of the extensions. It runs as follo
Externí odkaz:
http://arxiv.org/abs/2006.11018
Autor:
Crasta, Graziano, Fragalà, Ilaria
We prove that the Robin ground state and the Robin torsion function are respectively log-concave and $\frac{1}{2}$-concave on an uniformly convex domain $\Omega\subset \mathbb{R}^N$ of class $\mathcal{C}^m$, with $[m -\frac{ N}{2}]\geq 4$, provided t
Externí odkaz:
http://arxiv.org/abs/2006.07192