37 citations · 42 across the 17 of their papers we have counts for
22 papers
Kohler-Jobin inequality for -Laplace operator
Francesco Chiacchio, Vincenzo Ferone, Anna Mercaldo +1
A sharp lower bound for the first Dirichlet eigenvalue of the -laplacian is derived for sets with prescribed -torsional rigidity. The result provides an extension of the clas…
Weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders
Friedemann Brock, Francesco Chiacchio, Adele Ferone +1
In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.
Kohler-Jobin inequality for -Laplace operator in the Gauss space
Francesco Chiacchio, Vincenzo Ferone, Anna Mercaldo +1
A sharp lower bound for the first Dirichlet eigenvalue of the -laplacian in Gaussian space is derived for sets with prescribed generalized torsional rigidity. The result provide…
Singular elliptic equations having a gradient term with natural growth
A. Ferone, A. Mercaldo, S. Segura de León
We study a class of Dirichlet boundary value problems whose prototype is \begin{equation}\label{1.2abs} \left\{\begin{array}{ll} -Δ_p u =h(u)|\nabla u|^p+u^{q-1}+f(x)\, &\quad\hbox…
Shape of extremal functions for weighted Sobolev-type inequalities
Friedemann Brock, Francesco Chiacchio, Gisella Croce +1
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…
Isoperimetric sets for weighted twisted eigenvalues
Barbara Brandolini, Antoine Henrot, Anna Mercaldo +1
In tis paper we prove an isoperimetric inequality for the first twisted eigenvalue of a weighted operator, defined as the minimum of the usual Rayleigh quotient when…
Steiner symmetrization for anisotropic quasilinear equations via partial discretization
Friedemann Brock, Jesús Ildefonso Díaz, Adele Ferone +2
In this paper we obtain comparison results for the quasilinear equation with homogeneous Dirichlet boundary conditions by Steiner rearrangement in variabl…
Some isoperimetric inequalities with respect to monomial weights
Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2
We solve a class of isoperimetric problems on with respect to monomial weights. Let and be real numbers suc…
Finsler Hardy-Kato's inequality
Angelo Alvino, Adele Ferone, Anna Mercaldo +2
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 obtai…
Finsler Hardy inequalities
A. Mercaldo, M. Sano, F. Takahashi
In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a poi…
The isoperimetric problem for a class of non-radial weights and applications
Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2
We study a class of isoperimetric problems on where the densities of the weighted volume and weighted perimeter are given by two different non-radial function…
On weighted isoperimetric inequalities with non-radial densities
Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2
We consider a class of isoperimetric problems on where the volume and the area element carry two different weights of the type . We solve them in…
Uniqueness for Neumann problems for nonlinear elliptic equations
Maria Francesca Betta, Olivier Guibé, Anna Mercaldo
In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is --div((1 + |u| 2) (p--2)/2 u) -- div…
New Pólya-Szegö-type inequalities and an alternative approach to comparison results for PDE's
Friedemann Brock, Adele Ferone, Francesco Chiacchio +1
We prove some Pólya-Szegö type inequalities which involve couples of functions and their rearrangements. Our inequalities reduce to the classical Pólya-Szegö principle when the two…
Some isoperimetric inequalities on with respect to weights
A. Alvino, F. Brock, F. Chiacchio +2
We solve a class of isoperimetric problems on with respect to weights that are powers of the distance to the origin. For instance we show that if , then…
Symmetry and asymmetry of minimizers of a class of noncoercive functionals
F Brock, G Croce, O Guibé +1
In this paper we prove symmetry results for minimizers of a non coercive functional defined on the class of Sobolev functions with zero mean value. We prove that the minimizers are…
An isoperimetric inequality for Gauss--like product measures
Friedemann Brock, Francesco Chiacchio, Anna Mercaldo
This paper deals with various questions related to the isoperimetic problem for smooth positive measure , with . Firstly we find some neces…
Neumann problems for nonlinear elliptic equations with data
Maria Francesca Betta, Olivier Guibé, Anna Mercaldo
In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \begin{equation*} \begin{cases} -Δ_{p} u -\text{div} (c(x)|u…
A weighted isoperimetric inequality in a wedge
Friedemann Brock, Francesco Chiacchio, Anna Mercaldo
Let be non-negative numbers, and define a measure in the wedge by $dμ= e^{c|x|^2} x_1 ^{k_1}...x_N ^{k_N}…
On isoperimetric inequalities with respect to infinite measures
F. Brock, A. Mercaldo, M. R. Posteraro
We study isoperimetric problems with respect to infinite measures on . In the case of the measure defined by , , we prove that, among all sets…
Weighted isoperimetric inequalities in cones and applications
Friedemann Brock, Francesco Chiacchio, Anna Mercaldo
This paper deals with weighted isoperimetric inequalities relative to cones of . We study the structure of measures that admit as isoperimetric sets the intersectio…
Well-posed elliptic Neumann problems involving irregular data and domains
A. Alvino, A. Cianchi, V. Maz'ya +1
Nonlinear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continu…