A Bernoulli problem with non constant gradient boundary constraint

We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in the convex case, the existence of a subsolution guarantees the existence of a classical solution, which is proved to be convex.Comment: 8 pages, no figure

A note on an overdetermined problem for the capacitary potential

We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.Comment: 7 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

Wulff shape characterizations in overdetermined anisotropic elliptic problems

We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems

An overdetermined problem for the anisotropic capacity

We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in $\mathbb{R}^N$, establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of W. Reichel [Arch. Rational Mech. Anal. 137 (1997)], where the usual Newtonian capacity is considered, giving rise to an overdetermined problem for the standard Laplace equation. Here, we replace the usual Euclidean norm of the gradient with an arbitrary norm $H$. The resulting symmetry of the solution is that of the so-called Wulff shape (a ball in the dual norm $H_0$)

On the quantitative isoperimetric inequality in the plane with the barycentric distance

In this paper we study the following quantitative isoperimetric inequality in the plane: $\lambda_0^2(\Omega) \leq C \delta(\Omega)$ where $\delta$ is the isoperimetric deficit and $\lambda_0$ is the barycentric asymmetry. Our aim is to generalize some results obtained by B. Fuglede in \cite{Fu93Geometriae}. For that purpose, we consider the shape optimization problem: minimize the ratio $\delta(\Omega)/\lambda_0^2(\Omega)$ in the class of compact connected sets and in the class of convex sets

Patrimonios disonantes y memorias democráticas: una comparación entre Chile y España / Dissonant Heritage and Democratic Memories: a Comparison between Chile and Spain

En este artículo se comparan las políticas de memoria en Chile y España. Se establecen similitudes y diferencias en el ámbito de la gestión del patrimonio construido, a partir de algunos ejemplos de monumentos intencionales y no intencionales representativos del reciente pasado dictatorial. Se propone una lectura centrada en dos tipos de memoria pública “democrática” y se discute un modelo alternativo, que emerge de los diálogos académicos que conectan España y el Cono Sur. Palabras clave: Políticas de memoria, monumentos, patrimonio, Chile, España.This article compares politics of memory in Chile and Spain. It establishes similarities and differences in the management of built heritage, using examples of intentional and unintentional monuments that represent the dictatorial past. It proposes an interpretation centered in two different types of “democratic” memory and discusses an alternative model, which emerges from the academic dialogues that connect Spain and the Southern Cone. Keywords: Politics of Memory, Monuments, Heritage, Chile, Spain