Zobrazeno 1 - 10
of 215
pro vyhledávání: '"Nitsch, Carlo"'
We study the behaviour, as $p \to +\infty$, of the second eigenvalues of the $p$-Laplacian with Robin boundary conditions and the limit of the associated eigenfunctions. We prove that, up to some regularity of the set, the limit of the second eigenva
Externí odkaz:
http://arxiv.org/abs/2410.13356
Autor:
Acampora, Paolo, Celentano, Antonio, Cristoforoni, Emanuele, Nitsch, Carlo, Trombetti, Cristina
For every given $\beta<0$, we study the problem of maximizing the first Robin eigenvalue of the Laplacian $\lambda_\beta(\Omega)$ among convex (not necessarily smooth) sets $\Omega\subset\mathbb{S}^{n}$ with fixed perimeter. In particular, denoting b
Externí odkaz:
http://arxiv.org/abs/2407.05987
In this paper, we establish a comparison principle in terms of Lorentz norms and point-wise inequalities between a positive solution $u$ to the Poisson equation with non-homogeneous Neumann boundary conditions and a specific positive solution $v$ to
Externí odkaz:
http://arxiv.org/abs/2405.05392
Publikováno v:
Milan J. Math. (2024)
In this paper, we prove a Serrin-type result for an elliptic system of equations, overdetermined with both Dirichlet and a generalized Neumann conditions. With this tool, we characterize the critical shapes under volume constraint of some domain func
Externí odkaz:
http://arxiv.org/abs/2402.09817
Publikováno v:
SIAM J. Math. Anal.56(2024), no.3, 3509-3536
We are interested in the thermal insulation of a bounded open set $\Omega$ surrounded by a set whose thickness is locally described by $\varepsilon h$, where $h$ is a non-negative function defined on the boundary $\partial\Omega$. We study the proble
Externí odkaz:
http://arxiv.org/abs/2305.04078
Publikováno v:
Mathematische Annalen 12 April, 2024
In this paper, we introduce a symmetrization technique for the gradient of a $\BV$ function, which separates its absolutely continuous part from its singular part (sum of the jump and the Cantorian part). In particular, we prove an $\text{\emph{L}}^{
Externí odkaz:
http://arxiv.org/abs/2302.11332
Publikováno v:
ESAIM: COCV, 29 (2023) 3
We study the thermal insulation of a bounded body $\Omega\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a bulk layer of insulating material. We consider a model of heat transfer between the insulated body and the environment determin
Externí odkaz:
http://arxiv.org/abs/2205.03275
We study a shape optimization problem involving a solid $K\subset\mathbb{R}^n$ that is maintained at constant temperature and is enveloped by a layer of insulating material $\Omega$ which obeys a generalized boundary heat transfer law. We minimize th
Externí odkaz:
http://arxiv.org/abs/2112.07300
We study the behaviour, when $p \to +\infty$, of the first $p$-Laplacian eigenvalues with Robin boundary conditions and the limit of the associated eigenfunctions. We prove that the limit of the eigenfunctions is a viscosity solution to an eigenvalue
Externí odkaz:
http://arxiv.org/abs/2111.10107
In this paper we study the $\Gamma$-limit, as $p\to 1$, of the functional $$ J_{p}(u)=\frac{\displaystyle\int_\Omega |\nabla u|^p + \beta\int_{ \partial \Omega} |u|^p}{\displaystyle \int_\Omega |u|^p}, $$ where $\Omega$ is a smooth bounded open set i
Externí odkaz:
http://arxiv.org/abs/2110.15226