Arianna Giunti

activity

20152021

most citedDerivation of Darcy's law in randomly punctured domains

4 citations · 9 across the 12 of their papers we have counts for

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13 papers · 1 filter

math.AP2021

Edge States for generalised Iwatsuka models: Magnetic fields having a fast transition across a curve

Arianna Giunti, Juan J. L. Velázquez

In this paper, we study the localization and propagation properties of the edge states associated to a class of magnetic laplacians in $R^{2}$ . We assume that the intensity…

math.AP2021★ 4 cited

Derivation of Darcy's law in randomly punctured domains

Arianna Giunti

We consider the homogenization of a Poisson problem or a Stokes system in a randomly punctured domain with Dirichlet boundary conditions. We assume that the holes are spherical and…

math.AP2020

Convergence rates for the homogenization of the Poisson problem in randomly perforated domains

Arianna Giunti

In this paper we provide converge rates for the homogenization of the Poisson problem with Dirichlet boundary conditions in a randomly perforated domain of $R^{d}$ , $d \geq…

math.AP2020

Convergence of the pressure in the homogenization of the Stokes equations in randomly perforated domains

Arianna Giunti, Richard M. Höfer

We consider the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical h…

math.AP2019

Edge States for the magnetic Laplacian in domains with smooth boundary

Arianna Giunti, Juan J. L. Velázquez

We are interested in the spectral properties of the magnetic Schrödinger operator $H_{ε}$ in a domain $Ω \subset R^{2}$ with compact boundary and with magnetic field…

math.AP2019

On the existence of the Green function for elliptic systems in divergence form

Arianna Giunti, Felix Otto

We study the existence of the Green function for an elliptic system in divergence form $- \nabla \cdot a \nabla$ in $R^{d}$ , with $d > 2$ . The tensor field $a = a (x)$ is only assum…

math.AP2018

On the homogenization of random stationary elliptic operators in divergence form

Arianna Giunti, Juan J. L. Velázquez

In this note we comment on the homogenization of a random elliptic operator in divergence form $- \nabla \cdot a \nabla$ , where the coefficient field $a$ is distributed according to…

math.AP2018★ 2 cited

Homogenization for the Stokes equations in randomly perforated domains under almost minimal assumptions on the size of the holes

Arianna Giunti, Richard M. Höfer

We prove the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical hole…

math.AP2018

Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes

Arianna Giunti, Richard Höfer, Juan J. L. Velázquez

This paper deals with the homogenization of the Poisson equation in a bounded domain of $R^{d}$ , $d > 2$ , which is perforated by a random number of small spherical holes with…

math.AP2017

Effective Multipoles in Random media

Peter Bella, Arianna Giunti, Felix Otto

In a homogeneous medium, the far-field generated by a localized source can be expanded in terms of multipoles; the coefficients are determined by the moments of the localized charg…

math.AP2016

Green's function for elliptic systems: existence and Delmotte-Deuschel bounds

Joseph G. Conlon, Arianna Giunti, Felix Otto

We prove that for an open domain $D \subset R^{d}$ with $d \geq 2$ , for every (measurable) uniformly elliptic tensor field $a$ and for almost every point $y \in D$ , ther…

math.AP2015★ 1 cited

Green's function for elliptic systems: moment bounds

Peter Bella, Arianna Giunti

We study estimates of the Green's function in $R^{d}$ with $d \geq 2$ , for the linear second order elliptic equation in divergence form with variable uniformly elliptic coeff…

math.AP2015★ 2 cited

Quantitative stochastic homogenization: local control of homogenization error through corrector

Peter Bella, Arianna Giunti, Felix Otto

This note addresses the homogenization error for linear elliptic equations in divergence-form with random stationary coefficients. The homogenization error is measured by comparing…