Now showing items 12-31 of 195

• #### Asymptotic models for free boundary flow in porous media ﻿

(2019)
We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ...
• #### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation ﻿

(2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ...
• #### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation ﻿

(2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted W1,8 around a carefully chosen, two term ansatz. Such knowledge ...
• #### Bayesian approach to inverse scattering with topological priors ﻿

(2020)
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite ...
• #### Bilinear Calderón--Zygmund theory on product spaces ﻿

(2019-10)
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach ...
• #### Bilinear identities involving the $k$-plane transform and Fourier extension operators ﻿

(2019)
We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$-plane transform. As the estimates are $L^2$-based, they follow from ...
• #### Bilinear identities involving the k-plane transform and Fourier extension operators ﻿

(2019-11-30)
We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear ...
• #### Bilinear representation theorem ﻿

(2018-01-01)
We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ...
• #### Bilinear Spherical Maximal Functions of Product Type ﻿

(2021-08-12)
In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered ...
• #### A Bilinear Strategy for Calderón's Problem ﻿

(2019-08)
Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the ...
• #### A Bilinear Strategy for Calderón’s Problem ﻿

(2020-05)
Electrical Impedance Imaging would suffer a serious obstruction if two different conductivities yielded the same measurements of potential and current at the boundary. The Calderón’s problem is to decide whether the ...
• #### Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators ﻿

(2019-03-14)
Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ ...
• #### Bloom type upper bounds in the product BMO setting ﻿

(2019-04-08)
• #### A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores ﻿

(2021)
We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ...
• #### Convergence over fractals for the Schrödinger equation ﻿

(2021-01)
We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with ...