Publication

Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data

Publications associées (11)

Multiplicative chaos of the Brownian loop soup

Antoine Pierre François Jego, Titus Lupu

We construct a measure on the thick points of a Brownian loop soup in a bounded domain D

D

of the plane with given intensity theta>0

\theta >0

, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

WILEY2023

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, David Jean-Michel Candil, Cheuk Yin Lee

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

Springer2023

Multiplicative chaos of the Brownian loop soup

Antoine Pierre François Jego, Titus Lupu

We construct a measure on the thick points of a Brownian loop soup in a bounded domain D

D

of the plane with given intensity theta>0

\theta >0

, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

WILEY2023

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

A Note on BIBO Stability

Michaël Unser

The statements on the BIBO stability of continuoustime convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identi ...

2020

The hamburger theorem

Jan Kyncl

We generalize the ham sandwich theorem to d +1 measures on R-d as follows. Let mu(1), mu(2),..., mu(d+1) be absolutely continuous finite Borel measures on R-d. Let omega(i) = mu(i) (R-d) for i is an element of [d + 1], omega = min{omega(i) : i is an elemen ...

Elsevier Science Bv2018

Stochastic partial differential equations driven by Lévy white noises : generalized random processes, random field solutions and regularity

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Pointwise estimates and existence of solutions of porous medium and p-Laplace evolution equations with absorption and measure data

Quoc Hung Nguyen

Let Omega be a bounded domain of R-N (N >= 2). We obtain a necessary and a sufficient condition, expressed in terms of capacities, for the existence of a solution to the porous medium equation with absorption {u(t) - Delta (vertical bar u vertical bar(m-1) ...

Scuola Normale Superiore2016

On the coupling of 1D and 3D Diffusion-Reaction Equations: Application to Tissue Pefusion Problems

Alfio Quarteroni, Carlo D'Angelo

In this paper we consider the coupling between two diffusion-reaction problems, one taking place in a three-dimensional domain Ω, the other in a one-dimensional subdomain Λ. This coupled problem is the simplest model of fluid flow in a three-dimensional po ...

2008

Convolution Operators And Homomorphisms Of Locally Compact Groups

Let 1 < p < infinity, let G and H be locally compact groups and let c) be a continuous homomorphism of G into H. We prove, if G is amenable, the existence of a linear contraction of the Banach algebra CVp (G) of the p-convolution operators on G into CVp (H ...

Cambridge University Press2008