Publication

Estimates for the topological degree and related topics

Publications associées (11)

Single-Chain Nanoparticles for Intracellular Drug Delivery

Single-chain nanoparticles (SCNPs) are a type of polymeric nanoparticles formed by collapsing/folding individual polymer chains via intra-molecular interactions. Their emergence holds promise to construct sub-20 nm polymeric nanoparticles with defined stru ...

EPFL2022

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

On Hardy and Caffarelli-Kohn-Nirenberg inequalities

Hoài-Minh Nguyên

We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps f ...

2019

A refined estimate for the topological degree

Hoài-Minh Nguyên

We sharpen an estimate of [4] for the topological degree of continuous maps from a sphere Sdinto itself in the case d >= 2. This provides the answer for d >= 2 to a question raised by Brezis. The problem is still open for d = 1. (C) 2017 Academie des scien ...

2017

Scampi: a robust approximate message-passing framework for compressive imaging

Jean François Emmanuel Barbier, Florent Gérard Krzakala

Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an alternative probabil ...

Iop Publishing Ltd2016

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

Jan Sickmann Hesthaven, Paolo Gatto

The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that ...

Springer Verlag2015

Structure Tensor Total Variation

Michaël Unser, Stamatios Lefkimmiatis

We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure ...

SIAM2015

Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

Michaël Unser, Aurélien Bourquard, Hagay Kirshner, John Paul Ward

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and sto ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

IEEE2012

Infinite dimensional geodesic flows and the universal Teichmüller space

François Gay-Balmaz

The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...

EPFL2009

Quasilinear second order elliptic systems and topological degree

Hicham Georges Gebran

We consider a large class of quasilinear second order elliptic systems of the form - ∑α,β=1N aαβ(x,u(x)),∇u(x))∂2αβu(x) + b(x,u(x),∇u(x)) = 0, where x varies in an unbounded domain Ω of the Euclidean space RN and u = (u1,...,um) is a vector of functi ...

EPFL2005

Publications associées (11)

Single-Chain Nanoparticles for Intracellular Drug Delivery

Suiyang Liao

EPFL2022

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022