Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Pisante, Giovanni"'
We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by means of an
Externí odkaz:
http://arxiv.org/abs/2404.02086
We study a weighted eigenvalue problem with anisotropic diffusion in bounded Lipschitz domains $\Omega\subset \mathbb{R}^{N} $, $N\ge1$, under Robin boundary conditions, proving the existence of two positive eigenvalues $\lambda^{\pm}$ respectively a
Externí odkaz:
http://arxiv.org/abs/2303.01401
We fill the gap left open in \cite{MT}, regarding the minimum exponent on the logarithmic correction weight so that the Leray-Trudinger inequality (see \cite{PsSp}) holds. Instead of the representation formula used in \cite{PsSp} and \cite{MT}, our p
Externí odkaz:
http://arxiv.org/abs/2208.05430
In this note we prove the existence of a set $E_0\subset\mathbb{R}^2$, different from a ball, which minimizes, among the convex sets that satisfy a suitable interior cone condition, the ratio \begin{equation} \label{eq:0} \frac{D(E)}{\lambda_\mathcal
Externí odkaz:
http://arxiv.org/abs/2207.06370
In this paper, we study a reverse isoperimetric inequality for planar convex bodies whose radius of curvature is between two positive numbers 0 < $\alpha$ < $\beta$, called ($\alpha$, $\beta$)--convex bodies. We show that among planar ($\alpha$, $\be
Externí odkaz:
http://arxiv.org/abs/2107.14455
Publikováno v:
In Journal of Differential Equations 5 January 2024 378:303-338
In this paper we focus our attention on an embedding result for a weighted Sobolev space that involves as weight the distance function from the boundary taken with respect to a general smooth gauge function $F$. Starting from this type of inequalitie
Externí odkaz:
http://arxiv.org/abs/1902.02091
Autor:
Croce, Gisella, Pisante, Giovanni
We consider the vectorial system \[ \begin{cases} Du \in \mathcal{O}(2), & \mbox{a.e. in}\;\Omega, u=0, & \mbox{on} \;\partial \Omega, \end{cases} \] where $\Omega$ is a subset of $\R^2$, $u:\Omega\to \R^2$ and $\mathcal{O}(2)$ is the orthogonal grou
Externí odkaz:
http://arxiv.org/abs/1609.02743
Publikováno v:
Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 2017
For $\mathrm{H} \in C^2(\mathbb{R}^{N \times n})$ and $u : \Omega \subseteq \mathbb{R}^n \to \mathbb{R}^N$, consider the system \[ \label{1}\mathrm{A}\_\infty u\, :=\,\Big(\mathrm{H}\_P \otimes \mathrm{H}\_P + \mathrm{H}[\mathrm{H}\_P]^\bot \mathrm{H
Externí odkaz:
http://arxiv.org/abs/1604.04385
We prove higher differentiability of bounded local minimizers to some widely degenerate functionals, verifying superquadratic anisotropic growth conditions. In the two dimensional case, we prove that local minimizers to a model functional are locally
Externí odkaz:
http://arxiv.org/abs/1604.04189