Rémy Rodiac

activity

20152023

most citedHarmonic dipoles and the relaxation of the neo-Hookean energy in 3D elasticity

14 citations · 36 across the 20 of their papers we have counts for

collaborators

22 papers

math.AP2023★ 1 cited

A relaxation approach to the minimisation of the neo-Hookean energy in 3D

Marco Barchiesi, Duvan Henao, Carlos Mora-Corral +1

Despite its high significance in nonlinear elasticity, the neo-Hookean energy is still not known to admit minimisers in some appropriate admissible class. Using ideas from relaxati…

math.AP2022

On the Convergence of critical points of the Ambrosio-Tortorelli functional

Jean-François Babadjian, Vincent Millot, Rémy Rodiac

This work is devoted to study the asymptotic behavior of critical points ${(u_{ε}, v_{ε})}_{ε > 0}$ of the Ambrosio-Tortorelli functional. Under a uniform…

math.AP2022

The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length

Mickaël Dos Santos, Rémy Rodiac, Etienne Sandier

The aim of this article is to study the magnetic Ginzburg-Landau functional with an oscillating pinning term. We consider here oscillations of the pinning term that are much faster…

math.AP2021★ 1 cited

On the lack of compactness in the axisymmetric neo-Hookean model

Marco Barchiesi, Duvan Henao, Carlos Mora-Corral +1

We provide a fine description of the weak limit of sequences of regular axisymmetric maps with equibounded neo-Hookean energy, under the assumption that they have finite surface en…

math.AP2021

Interacting helical traveling waves for the Gross-Pitaevskii equation

Juan Dávila, Manuel del Pino, María Medina +1

We consider the 3D Gross-Pitaevskii equation \begin{equation}\nonumber i\partial_t ψ+Δψ+(1-|ψ|^2)ψ=0 \text{ for } ψ:\mathbb{R}\times \mathbb{R}^3 \rightarrow \mathbb{C} \end{equati…

math.AP2021★ 14 cited

Harmonic dipoles and the relaxation of the neo-Hookean energy in 3D elasticity

Marco Barchiesi, Duvan Henao, Carlos Mora-Corral +1

We consider the problem of minimizing the neo-Hookean energy in $3D$. The difficulty of this problem is that the space of maps without cavitation is not compact, as shown by Cont…

math.AP2020

Renormalized energies for unit-valued harmonic maps in multiply connected domains

Rémy Rodiac, Paúl Ubillús

In this article we derive the expression of \textit{renormalized energies} for unit-valued harmonic maps defined on a smooth bounded domain in $\mathbb{R}^2$ whose boundary has s…

math.AP2020★ 3 cited

Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold

Antonin Monteil, Rémy Rodiac, Jean Van Schaftingen

We study the asymptotic behaviour, as a small parameter $ε$ tends to zero, of minimisers of a Ginzburg-Landau type energy with a nonlinear penalisation potential vanishin…

math.AP2020

Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains

Antonin Monteil, Rémy Rodiac, Jean Van Schaftingen

We define renormalised energies for maps that describe the first-order asymptotics of harmonic maps outside of singularities arising due to obstructions generated by the boundary d…

math.AP2019★ 1 cited

Metric characterization of the sum of fractional Sobolev spaces

Rémy Rodiac, Jean Van Schaftingen

We introduce a non-linear criterion which allows us to determine when a function can be written as a sum of functions belonging to homogeneous fractional spaces: for $\ell \in \mat…

math.AP2019★ 5 cited

Interacting helical vortex filaments in the 3-dimensional Ginzburg-Landau equation

Juan Dávila, Manuel del Pino, Maria Medina +1

For each given $n \geq 2$ , we construct a family of entire solutions $u_{ε} (z, t)$ , $ε > 0$ , with helical symmetry to the 3-dimensional complex-valued Ginzburg-Landa…

math.FA2018★ 5 cited

Critical weak- $L^{p}$ differentiability of singular integrals

Luigi Ambrosio, Augusto C. Ponce, Rémy Rodiac

We establish that for every function $u \in L_{loc}^{1} (Ω)$ whose distributional Laplacian $Δ u$ is a signed Borel measure in an open set $Ω$ in $R^{N}$ , the distribut…

math.AP2018

Description of limiting vorticities for the magnetic 2D Ginzburg-Landau equations

Rémy Rodiac

Let $Ω$ be a bounded open set in $R^{2}$ . The aim of this article is to describe the functions $h$ in $H^{1} (Ω)$ and the Radon measures $μ$ which satisfy $- Δ h + h = μ$ and $ div(T…

math.AP2017★ 2 cited

One dimensional phase transition problem modelling striped spin orbit coupled Bose-Einstein condensates

Amandine Aftalion, Rémy Rodiac

We study the behaviour of a Modica-Mortola phase transition type problem with a non-homogeneous Neumann boundary condition. According to the parameters of the problem, this leads t…

math.AP2017★ 2 cited

Epsilon-regularity for p-harmonic maps at a free boundary on a sphere

Katarzyna Mazowiecka, Rémy Rodiac, Armin Schikorra

We prove an $ε$ -regularity theorem for vector-valued p-harmonic maps, which are critical with respect to a partially free boundary condition, namely that they map the boundary into…

math.AP2017

Variational reduction for semi-stiff Ginzburg-Landau vortices

Rémy Rodiac

Let $Ω$ be a smooth bounded domain in $R^{2}$ . For $ε > 0$ small, we construct non-constant solutions to the Ginzburg-Landau equations $- Δ u = \frac{1}{ε ^{2}} (1 - ∣ u ∣^{2}) u$ in $Ω$ suc…

math.AP2016

On the existence of minimizers for the neo-Hookean energy in the axisymmetric setting

Duvan Henao, Rémy Rodiac

Let $Ω$ be a smooth bounded axisymmetric set in $R^{3}$ . In this paper we investigate the existence of minimizers of the so-called neo-Hookean energy among a class of axisymmetric m…

math.AP2016★ 1 cited

On the convergence of minimizers of singular perturbation functionals

Andres Contreras, Xavier Lamy, Rémy Rodiac

The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit pl…

math.AP2015

Boundary regularity of weakly anchored harmonic maps

Andres Contreras, Xavier Lamy, Rémy Rodiac

In this note we study the boundary regularity of minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularit…

math.AP2015

Regularity properties of stationary harmonic functions whose Laplacian is a Radon measure

Rémy Rodiac

We study the regularity of Radon measures $μ$ which satisfy that there exists a function $h_{μ}$ in $H^{1} (Ω)$ , stationary harmonic such that $Δ h_{μ} = μ$ in $Ω$ (here $Ω$ is an open set o…

math.AP2015

Existence and non existence results for minimizers of the Ginzburg-Landau energy with prescribed degrees

Mickaël Dos Santos, Rémy Rodiac

Let $D = Ω ∖ ω ˉ \subset R^{2}$ be a smooth annular type domain. We consider the simplified Ginzburg-Landau energy $E_ε(u)=\frac{1}{2}\int_{\mathcal{D}} |\n…

math.AP2015★ 1 cited

Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids

Laurent Hauswirth, Rémy Rodiac

Let $A \subset R^{2}$ be a smooth doubly connected domain. We consider the Dirichlet energy $E (u) = \int_{A} ∣\nabla u ∣^{2}$ , where $u : A \to C$ , and look for…

A relaxation approach to the minimisation of the neo-Hookean energy in 3D

On the Convergence of critical points of the Ambrosio-Tortorelli functional

The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length

On the lack of compactness in the axisymmetric neo-Hookean model

Interacting helical traveling waves for the Gross-Pitaevskii equation

Harmonic dipoles and the relaxation of the neo-Hookean energy in 3D elasticity

Renormalized energies for unit-valued harmonic maps in multiply connected domains

Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold

Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains

Metric characterization of the sum of fractional Sobolev spaces

Interacting helical vortex filaments in the 3-dimensional Ginzburg-Landau equation

Critical weak-Lp differentiability of singular integrals

Description of limiting vorticities for the magnetic 2D Ginzburg-Landau equations

One dimensional phase transition problem modelling striped spin orbit coupled Bose-Einstein condensates

Epsilon-regularity for p-harmonic maps at a free boundary on a sphere

Variational reduction for semi-stiff Ginzburg-Landau vortices

On the existence of minimizers for the neo-Hookean energy in the axisymmetric setting

On the convergence of minimizers of singular perturbation functionals

Boundary regularity of weakly anchored harmonic maps

Regularity properties of stationary harmonic functions whose Laplacian is a Radon measure

Existence and non existence results for minimizers of the Ginzburg-Landau energy with prescribed degrees

Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids

Critical weak- $L^{p}$ differentiability of singular integrals