Mircea Petrache

activity

20092026

most citedNext Order Asymptotics and Renormalized Energy for Riesz Interactions

93 citations · 187 across the 31 of their papers we have counts for

collaborators

Showing math.APShow all

8 papers · 1 filter

math.AP2024

Existence and uniqueness of Monge minimizers for a Multi-marginal Optimal Transport problem with intermolecular interactions cost

Augusto Gerolin, Mircea Petrache, Adolfo Vargas-Jimenez

We investigate a new multi-marginal optimal transport problem arising from a dissociation model in the Strong Interaction Limit of Density Functional Theory. In this short note, we…

math.AP2019

Crystallization to the square lattice for a two-body potential

Laurent Bétermin, Lucia De Luca, Mircea Petrache

We consider two-dimensional zero-temperature systems of $N$ particles to which we associate an energy of the form $E [V] (X) := 1 \leq i < j \leq N \sum V (∣ X (i) - X (j) ∣),$ where…

math.AP2019

Cyclically monotone non-optimal $N$ -marginal transport plans and Smirnov-type decompositions for $N$ -flows

Mircea Petrache

In the setting of optimal transport with $N \geq 2$ marginals, a necessary condition for transport plans to be optimal is that they are $c$ -cyclically monotone. For $N = 2$ there exist…

math.AP2017★ 21 cited

The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness

Manuel V. Gnann, Mircea Petrache

We consider the thin-film equation $\partial_{t} h + \nabla \cdot (h^{2} \nablaΔ h) = 0$ in physical space dimensions (i.e., one dimension in time $t$ and two lateral dimens…

math.AP2010

An integrability result for $L^{p}$ -vectorfields in the plane

Mircea Petrache

We prove that if $p > 1$ then the divergence of a $L^{p}$ -vectorfield $V$ on a 2-dimensional domain $Ω$ is the boundary of an integral 1-current, if and only if $V$ can be represented…

math.AP2010

Weak closure of Singular Abelian $L^{p}$ -bundles in $3$ dimensions

Mircea Petrache, Tristan Rivière

We prove the closure for the sequential weak $L^{p}$ -topology of the class of vectorfields on $B^{3}$ having integer flux through almost every sphere. We show how this problem is conne…

math.AP2010

Existence of solutions to a higher dimensional mean-field equation on manifolds

Luca Martinazzi, Mircea Petrache

For $m \geq 1$ we prove an existence result for the equation $(- Δ_{g})^{m} u + λ = λ \frac{e ^{2 m u}}{\int _{M} e ^{2 m u} d μ _{g}}$ on a closed Riemannian manifold $(M, g)$ of dimension $2 m$ for certa…

math.AP2009★ 13 cited

Asymptotics and quantization for a mean-field equation of higher order

Luca Martinazzi, Mircea Petrache

Given a regular bounded domain $Ω \subset R 2 m$ , we describe the limiting behavior of sequences of solutions to the mean field equation of order $2 m$ , $m \geq 1$ , $$(-Δ)^m u=ρ\frac{…

Existence and uniqueness of Monge minimizers for a Multi-marginal Optimal Transport problem with intermolecular interactions cost

Crystallization to the square lattice for a two-body potential

Cyclically monotone non-optimal N-marginal transport plans and Smirnov-type decompositions for N-flows

The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness

An integrability result for Lp-vectorfields in the plane

Weak closure of Singular Abelian Lp-bundles in 3 dimensions

Existence of solutions to a higher dimensional mean-field equation on manifolds

Asymptotics and quantization for a mean-field equation of higher order

Cyclically monotone non-optimal $N$ -marginal transport plans and Smirnov-type decompositions for $N$ -flows

An integrability result for $L^{p}$ -vectorfields in the plane

Weak closure of Singular Abelian $L^{p}$ -bundles in $3$ dimensions