F. Brock

activity

20112026

most citedA weighted isoperimetric inequality in a wedge

2 citations · 5 across the 15 of their papers we have counts for

collaborators

20 papers

math.AP2026

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.

math.AP2025

Isoperimetric Bounds for Weighted Steklov Eigenvalues with Radial Weights

Friedemann Brock, Francesco Chiacchio

We study the following class of Steklov eigenvalue problems: \[ \nabla \cdot \bigl( w \nabla u \bigr) = 0 \quad \text{in } Ω, \qquad \frac{\partial u}{\partial ν} = γv u \quad \tex…

math.AP2025

On the reverse isoperimetric inequality in Gauss space

Friedemann Brock, Francesco Chiacchio

In this paper we investigate the reverse isoperimetric inequality with respect to the Gaussian measure for convex sets in $R^{2}$ . While the isoperimetric problem for the…

math.OC2023

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…

math.AP2019★ 1 cited

Symmetry and stability of non-negative solutions to degenerate elliptic equations in a ball

Friedemann Brock, Peter Takac

We consider non-negative distributional solutions $u \in C^{1} (B_{R} ˉ)$ to the equation $-\mbox{div} [g(|\nabla u|)|\nabla u|^{-1} \nabla u ] = f(|x|,u)$ in a ball $B_{R}$ , with $…

math.AP2019

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 $- Δ_{p, x} u - u_{y y} = f$ with homogeneous Dirichlet boundary conditions by Steiner rearrangement in variabl…

math.AP2019

Some isoperimetric inequalities with respect to monomial weights

Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2

We solve a class of isoperimetric problems on $R_{+}^{2} := {(x, y) \in R^{2} : y > 0}$ with respect to monomial weights. Let $α$ and $β$ be real numbers suc…

math.AP2019

A unified approach to symmetry for semilinear equations associated to the Laplacian in $R^{N}$

Andres I. Avila, Friedemann Brock

We show radial symmetry of positive solutions to the Hénon equation $- Δ u = ∣ x ∣^{- ℓ} u^{q}$ in $R^{N} ∖ {0}$ , where $ℓ \geq 0$ , $q > 0$ and satisfy further tec…

math.AP2019

Some weighted isoperimetric problems on $R_{+}^{N}$ with stable half balls have no solutions

Friedemann Brock, Francesco Chiacchio

We show the counter-intuitive fact that some weighted isoperimetric problems on the half-space $R_{+}^{N}$ , for which half-balls centered at the origin are stable, have no…

math.AP2018

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 $R_{+}^{N}$ where the densities of the weighted volume and weighted perimeter are given by two different non-radial function…

math.AP2018

On weighted isoperimetric inequalities with non-radial densities

Angelo Alvino, Friedemann Brock, Francesco Chiacchio +2

We consider a class of isoperimetric problems on $R_{+}^{N}$ where the volume and the area element carry two different weights of the type $∣ x ∣^{l} x_{N}^{α}$ . We solve them in…

math.AP2017

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…

math.FA2016

Some isoperimetric inequalities on $R^{N}$ with respect to weights $∣ x ∣^{α}$

A. Alvino, F. Brock, F. Chiacchio +2

We solve a class of isoperimetric problems on $R^{N}$ with respect to weights that are powers of the distance to the origin. For instance we show that if $k \in [0, 1]$ , then…

math.AP2016

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…

math.AP2015

Symmetry for a general class of overdetermined elliptic problems

Friedemann Brock

Let $Ω$ be a bounded domain in $R^{N}$ , and let $u \in C^{1} (Ω)$ be a weak solution of the following overdetermined BVP: $-\nabla (g(|\nabla u|)|\nabla u|^{-1} \…

math.AP2015

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 $d μ = φ (x) d x$ , with $x \in Ω \subset R^{N}$ . Firstly we find some neces…

math.AP2014★ 1 cited

Optimal Szegö-Weinberger type inequalities

F. Brock, F. Chiacchio, G. di Blasio

Denote with $μ_{1} (Ω; e^{h (∣ x ∣)})$ the first nontrivial eigenvalue of the Neumann problem \begin{equation*} \left\{\begin{array}{lll} -\text{div}\left(e^{h\left(|x|\right…

math.AP2012★ 2 cited

A weighted isoperimetric inequality in a wedge

Friedemann Brock, Francesco Chiacchio, Anna Mercaldo

Let $c, k_{1}, ..., k_{N}$ be non-negative numbers, and define a measure $μ$ in the wedge $W := {x \in R^{N} : x_{i} > 0, i = 1, ..., N}$ by $dμ= e^{c|x|^2} x_1 ^{k_1}...x_N ^{k_N}…

math.AP2011★ 1 cited

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 $R^{n}$ . In the case of the measure $μ$ defined by $d μ = e^{c ∣ x ∣^{2}} d x$ , $c \geq 0$ , we prove that, among all sets…

math.AP2011

Weighted isoperimetric inequalities in cones and applications

Friedemann Brock, Francesco Chiacchio, Anna Mercaldo

This paper deals with weighted isoperimetric inequalities relative to cones of $R^{N}$ . We study the structure of measures that admit as isoperimetric sets the intersectio…

Weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders

Isoperimetric Bounds for Weighted Steklov Eigenvalues with Radial Weights

On the reverse isoperimetric inequality in Gauss space

Shape of extremal functions for weighted Sobolev-type inequalities

Symmetry and stability of non-negative solutions to degenerate elliptic equations in a ball

Steiner symmetrization for anisotropic quasilinear equations via partial discretization

Some isoperimetric inequalities with respect to monomial weights

A unified approach to symmetry for semilinear equations associated to the Laplacian in RN

Some weighted isoperimetric problems on R+N​ with stable half balls have no solutions

The isoperimetric problem for a class of non-radial weights and applications

On weighted isoperimetric inequalities with non-radial densities

New Pólya-Szegö-type inequalities and an alternative approach to comparison results for PDE's

Some isoperimetric inequalities on RN with respect to weights ∣x∣α

Symmetry and asymmetry of minimizers of a class of noncoercive functionals

Symmetry for a general class of overdetermined elliptic problems

An isoperimetric inequality for Gauss--like product measures

Optimal Szegö-Weinberger type inequalities

A weighted isoperimetric inequality in a wedge

On isoperimetric inequalities with respect to infinite measures

Weighted isoperimetric inequalities in cones and applications

A unified approach to symmetry for semilinear equations associated to the Laplacian in $R^{N}$

Some weighted isoperimetric problems on $R_{+}^{N}$ with stable half balls have no solutions

Some isoperimetric inequalities on $R^{N}$ with respect to weights $∣ x ∣^{α}$