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A logarithmic epiperimetric inequality for the obstacle problem

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A logarithmic epiperimetric inequality for the obstacle problem

Maria Colombo

We study the regularity of the regular and of the singular set of the obstacle problem in any dimension. Our approach is related to the epiperimetric inequality of Weiss (Invent Math 138:23-50, Wei99a), which works at regular points and provides an alterna ...

2018

On the theory of drainage area for regular and non-regular points

Sara Bonetti

The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrological fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its comp ...

2018

Corpora Delicti

Alexandre Blanc, Marco Bakker

CORPORA DELICTI, The Significant Detail. The Corpus Delicti is the evidence of a crime. The term denotes the formation of a proof that allows the unmasking of a perpetrator. In the realm of interpretation and language, it could reveal matter on which an ac ...

MANSLAB2017

Logarithmic estimates for continuity equations

Maria Colombo

The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [7] concerning existence and uniqueness of renormalized solutions of continuity equations with unbounded damping coefficient. ...

2016

Cloaking using complementary media in the quasistatic regime

Hoài-Minh Nguyên

Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence the ellipticity ...

2016

In this paper we give a new proof of the ELSV formula. First, we refine an argument of Okounkov and Pandharipande in order to prove (quasi-)polynomiality of Hurwitz numbers without using the ELSV formula (the only way to do that before used the ELSV formul ...

Academic Press Inc Elsevier Science2015

Superlensing using complementary media

Hoài-Minh Nguyên

This paper studies magnifying superlens using complementary media. Superlensing using complementary media was suggested by Veselago in [16] and innovated by Nicorovici et al. in [9] and Pendry in [10]. The study of this problem is difficult due to two fact ...

Gauthier-Villars/Editions Elsevier2015

Audio Steganography using Convex Demixing

Yann Mikaël Schoenenberger

In the first part, we first introduce steganography (in chapter 1) not in the usual context of information security, but as a method to piggyback data on top of some content. We then focus on audio steganography and propose a new steganographic scheme in c ...

2014

Lifting simplicial complexes to the boundary of convex polytopes

Lionel Pournin

Abstract: A simplicial complex C on a d-dimensional configuration of n points is k-regular if its faces are projected from the boundary complex of a polytope with dimension at most d+k. Since C is obviously (n-d-1)-regular, the set of all integers k for wh ...

Elsevier2012

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

Maria Colombo

We prove that solutions of a mildly regularized Perona–Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the gener ...

2012