Publications by Maria Colombo | EPFL Graph Search

Optimal regularity for the fully nonlinear thin obstacle problem

Maria Colombo, Xavier Fernandez-Real Girona

In this work, we establish the optimal regularity for solutions to the fully nonlinear thin obstacle problem. In particular, we show the existence of an optimal exponent αF such that u is C1,αF on either side of the obstacle. In order to do that, we prove ...

2025

Infinite-width limit of deep linear neural networks

Maria Colombo, Lénaïc Chizat, Xavier Fernandez-Real Girona

This paper studies the infinite-width limit of deep linear neural networks (NNs) initialized with random parameters. We obtain that, when the number of parameters diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a ...

Hoboken2024

Oleinik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit

Maria Colombo, Nicola De Nitti

We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term W := 1(-infinity,0](center dot)exp(center dot) * rho satisfy an Oleinik-type entropy condition. More precisely, under different ...

WORLD SCIENTIFIC PUBL CO PTE LTD2024

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Maria Colombo, Silja Noëmi Aline Haffter

We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; ...

MATHEMATICAL SCIENCE PUBL2023

Anomalous Dissipation and Lack of Selection in the Obukhov-Corrsin Theory of Scalar Turbulence

Maria Colombo, Massimo Sorella

The Obukhov-Corrsin theory of scalar turbulence [21, 54] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov's K41 theory of fully developed turbulence [4 ...

Springernature2023

Gluing Non-unique Navier-Stokes Solutions

Maria Colombo

We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-uniqueness discovered by the authors in [1]. ...

Springernature2023

On the commutativity of flows of rough vector fields

Maria Colombo, Riccardo Tione

In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

ELSEVIER2022

Typicality results for weak solutions of the incompressible Navier-Stokes equations

Maria Colombo, Luigi De Rosa, Massimo Sorella

In this work we show that, in the class of L-infinity((0,T); L-2(T-3)) distributional solutions of the incompressible Navier-Stokes system, the ones which are smooth in some open interval of times are meagre in the sense of Baire category, and the Leray on ...

EDP SCIENCES S A2022

Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Maria Colombo

We prove non-uniqueness for a class of weak solutions to the Navier???Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1. ...

2022

Neuromuscular electrical stimulation restores upper limb sensory-motor functions and body representations in chronic stroke survivors

Olaf Blanke, Silvestro Micera, Andrea Crema, Andrea Serino, Michela Bassolino, Maria Colombo

2022

Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves

Maria Colombo, Camillo De Lellis

The seminal work of DiPerna and Lions (Invent Math 98(3):511-547, 1989) guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suitable selection of trajectories of the related ODE satisfying addition ...

2021

Mixing and diffusion for rough shear flows

Klaus Martin Widmayer, Maria Colombo

This article addresses mixing and diffusion properties of passive scalars advected by rough (

C^\alpha

) shear flows. We show that in general, one cannot expect a rough shear flow to increase the rate of inviscid mixing to more than that of a smooth shear ...

2021

On the Well-Posedness of Branched Transportation

Maria Colombo

We show in full generality the stability of optimal transport paths in branched transport: namely, we prove that any limit of optimal transport paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book Optimal trans ...

2021

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem

Maria Colombo

We answer a question left open in [4] and [3], by proving that the blow-up of minimizers u of the lower dimensional obstacle problem is unique at generic point of the free boundary. ...

2021

Regularity In Time Of Holder Solutions Of Euler And Hypodissipative Navier-Stokes Equations

Maria Colombo, Luigi De Rosa

In this work we investigate some regularization properties of the incompressible Euler equations and of the fractional Navier-Stokes equations where the dissipative term is given by (-Delta)(alpha) for a suitable power alpha is an element of (0, 1/2) (the ...

SIAM PUBLICATIONS2020

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020

Continuity Of Multimarginal Optimal Transport With Repulsive Cost

Maria Carola Colombo, Maria Colombo, Federico Stra

We provide sharp conditions for the finiteness and the continuity of multimarginal optimal transport with repulsive cost, expressed in terms of a suitable concentration property of the measure. To achieve this result, we analyze the Kantorovich potentials ...

2019

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Maria Colombo, Luigi Forcella, Luigi De Rosa

Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...

IOP2019