Zobrazeno 1 - 10
of 135
pro vyhledávání: '"Mercaldo, Anna"'
We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We
Externí odkaz:
http://arxiv.org/abs/2311.01083
In tis paper we prove an isoperimetric inequality for the first twisted eigenvalue $\lambda_{1,\gamma}^T(\Omega)$ of a weighted operator, defined as the minimum of the usual Rayleigh quotient when the trial functions belong to the weighted Sobolev sp
Externí odkaz:
http://arxiv.org/abs/2302.07774
Publikováno v:
Annales de l'Institut Henri Poincar{\'{e}} C, Analyse non lin{\'{e}}aire, 38 (2), 2021
In this paper we obtain comparison results for the quasilinear equation $-\Delta_{p,x} u - u_{yy} = f$ with homogeneous Dirichlet boundary conditions by Steiner rearrangement in variable $x$, thus solving a long open problem. In fact, we study a broa
Externí odkaz:
http://arxiv.org/abs/1912.02080
Autor:
Alvino, Angelo, Brock, Friedemann, Chiacchio, Francesco, Mercaldo, Anna, Posteraro, Maria Rosaria
We solve a class of isoperimetric problems on $\mathbb{R}^2_+ :=\left\{ (x,y)\in \mathbb{R} ^2 : y>0 \right\}$ with respect to monomial weights. Let $\alpha $ and $\beta $ be real numbers such that $0\le \alpha <\beta+1$, $\beta\le 2 \alpha$. We show
Externí odkaz:
http://arxiv.org/abs/1907.03659
Autor:
Betta, M. Francesca1 (AUTHOR) mfrancesca.betta@uniparthenope.it, Mercaldo, Anna2 (AUTHOR) mercaldo@unina.it, Volpicelli, Roberta2 (AUTHOR)
Publikováno v:
Mathematics (2227-7390). Feb2024, Vol. 12 Issue 3, p409. 15p.
We prove an improved version of the trace-Hardy inequality, so-called Kato's inequality, on the half-space in Finsler context. The resulting inequality extends the former one obtained by \cite{AFV} in Euclidean context. Also we discuss the validity o
Externí odkaz:
http://arxiv.org/abs/1807.03497
Autor:
Alvino, Angelo, Brock, Friedemann, Chiacchio, Francesco, Mercaldo, Anna, Posteraro, Maria Rosaria
We study a class of isoperimetric problems on $\mathbb{R}^{N}_{+} $ where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type $|x|^k x_N^\alpha$. Our results imply some sharp functio
Externí odkaz:
http://arxiv.org/abs/1805.02518
Autor:
Alvino, Angelo, Brock, Friedemann, Chiacchio, Francesco, Mercaldo, Anna, Posteraro, Maria Rosaria
We consider a class of isoperimetric problems on $\mathbb{R}^{N}_{+} $ where the volume and the area element carry two different weights of the type $|x|^lx_N^\alpha$. We solve them in a special case while a more detailed study is contained in \cite{
Externí odkaz:
http://arxiv.org/abs/1804.02282
In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is --div((1 + |$\nabla$u| 2) (p--2)/2 $\nabla$u) -- div(c(x)|u| p--2 u) = f in $\Omega$, (1 + |$\nabla$u| 2) (p--2)/2 $\nabla
Externí odkaz:
http://arxiv.org/abs/1712.03013
We prove some P\'olya-Szeg\"o type inequalities which involve couples of functions and their rearrangements. Our inequalities reduce to the classical P\'olya-Szeg\"o principle when the two functions coincide. As an application, we give a different pr
Externí odkaz:
http://arxiv.org/abs/1704.01898