33 citations · 201 across the 15 of their papers we have counts for
16 papers
Recovering nonsmooth coefficients for higher-order perturbations of a polyharmonic operator
Russell M. Brown, Landon Gauthier, Daniel Faraco
We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator with . We show that the map from the c…
Estimates for more Brascamp-Lieb forms in -spaces with power weights
Russell M. Brown, Katharine A. Ott
We consider a class of Brascamp-Lieb forms and give conditions which guarantee the boundedness of these form on -spaces with weights that are a power of the distance to the or…
Extendability of functions with partially vanishing trace
Sebastian Bechtel, Russell M. Brown, Robert Haller-Dintelmann +1
Let be open and be a closed part of its boundary. Under very mild assumptions on , we construct a bounded Sobolev extension oper…
Estimates for the -mixed problem in -domains
R. M. Brown, L. D. Croyle
We consider the -mixed problem in domains in with -boundary. We assume that the boundary between the sets where we specify Neumann and Dirichlet data is…
Estimates for Brascamp-Lieb forms in spaces with power weights
Russell M. Brown, Carl W. Lee, Katharine A. Ott
We establish a set of necessary conditions and a set of sufficient conditions for boundedness of a family of Brascamp-Lieb forms in Lorentz spaces and -spaces with power weigh…
Soliton Solutions and their (In)stability for the Focusing Davey-Stewartson II Equation
Peter A. Perry
We give a rigorous mathematical analysis of the one-soliton solution of the focusing Davey-Stewartson II equation and a proof of its instability under perturbation. Building on the…
Action of a scattering map on weighted Sobolev spaces in the plane
R. M. Brown, K. A. Ott, P. A. Perry
We consider a scattering map that arises in the -approach to the scattering theory for the Davey-Stewartson II equation and show that the map is an invertible map b…
The Green function for the mixed problem for the linear Stokes system in domains in the plane
K. A. Ott, S. Kim, R. M. Brown
We construct the Green function for the mixed boundary value problem for the linear Stokes system in a two-dimensional Lipschitz domain.
Heat kernel for the elliptic system of linear elasticity with boundary conditions
Justin Taylor, Seick Kim, Russell Brown
We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system…
The mixed problem for the Lamé system in two dimensions
Katharine A. Ott, Russell M. Brown
We consider the mixed problem for the Lamé system of elasticity in a bounded Lipschitz domain . We suppose that the boundary is written as the union of two…
The Green function for elliptic systems in two dimensions
J. L. Taylor, S. Kim, R. M. Brown
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 s…
The mixed problem in Lipschitz domains with general decompositions of the boundary
Justin L. Taylor, Katharine A. Ott, Russell M. Brown
This paper continues the study of the mixed problem for the Laplacian. We consider a bounded Lipschitz domain , , with boundary that is decomposed as $\p…
Estimates for a family of multi-linear forms
Zhongyi Nie, Russell Brown
We consider a special class of the multi-linear forms studied by Brascamp and Lieb. For these forms, we are able to characterize the L^p spaces for which the form is bounded. We us…
The mixed problem for the Laplacian in Lipschitz domains
Katharine A. Ott, Russell M. Brown
We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neum…
The mixed problem in L^p for some two-dimensional Lipschitz domains
Loredana Lanzani, Luca Capogna, Russell Brown
We consider the mixed problem for the Laplace operator in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. The boundary of the domain is deco…
Estimates for the scattering map associated to a two-dimensional first order system
Russell M. Brown
We consider the scattering transform for the first order system in the plane, (D-Q) ψ=0 where D is the 2x2 diagonal matrix differential operator whose diagonal entries are d-bar an…