arXiv subjects

R. M. Brown

Publications and source records attributed to R. M. Brown.

7 recordsLinked to original sources

arXiv2025

Inverse boundary value problems for polyharmonic operators with non-smooth coefficients

We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.

math.AP↗

arXiv2023

An estimate arising in scattering theory

We prove a decay estimate for an operator that arises in two-dimensional scattering problem.

math.AP↗

arXiv2019

Estimates for the $L^q$-mixed problem in $C^{1,1}$-domains

We consider the $L^q$-mixed problem in domains in ${\bf R}^n$ with $C^ {1,1}$-boundary. We assume that the boundary between the sets where we specify Neumann and Dirichlet data is Lipschitz. With these assumptions, we show that we may solve the $L^q$-mixed problem for $q$ in the range $1<q < n/(n-1)$.

math.AP↗

arXiv2016

Action of a scattering map on weighted Sobolev spaces in the plane

We consider a scattering map that arises in the $\bar \partial $-approach to the scattering theory for the Davey-Stewartson II equation and show that the map is an invertible map between certain weighted $L^2$ Sobolev spaces.

math.AP↗

arXiv2013

The Green function for the mixed problem for the linear Stokes system in domains in the plane

We construct the Green function for the mixed boundary value problem for the linear Stokes system in a two-dimensional Lipschitz domain.

math.AP↗

arXiv2012

The Green function for elliptic systems in two dimensions

We construct the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. We consider the elliptic system in a Lipschitz domain with mixed boundary conditions. Thus we specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We require a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary conditions. Our proof proceeds by defining a variant of the space $BMO(\partial Ω)$ that is adapted to the boundary conditions and showing that the solution exists in this space. We also give a construction of the Green function with Neumann boundary conditions and the fundamental solution in the plane.

math.AP↗

arXiv2009

Radiation hardness qualification of PbWO4 scintillation crystals for the CMS Electromagnetic Calorimeter

Ensuring the radiation hardness of PbWO4 crystals was one of the main priorities during the construction of the electromagnetic calorimeter of the CMS experiment at CERN. The production on an industrial scale of radiation hard crystals and their certification over a period of several years represented a difficult challenge both for CMS and for the crystal suppliers. The present article reviews the related scientific and technological problems encountered.

physics.ins-det↗