Russell M. Brown

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The purpose of this note is to establish a small extension of a result of Panchenko, Päivärinta and Uhlmann [14]. These authors recently showed that we have uniqueness in the inverse conductivity problem for conductivities which are in the class C 3/2 in three dimensions and higher. This built on earlier work of one the authors, Brown [3]. In this note, we(More)
Let Ω be a domain in R n whose boundary is C 1 if n ≥ 3 or C 1,β if n = 2. We consider a magnetic Schrödinger operator L W,q in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for L W,q. We also consider a steady state heat equation with convection term ∆+2W ·∇ and recover(More)
We consider the mixed problem,      ∆u = 0 in Ω ∂u ∂ν = f N on N u = f D on D in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data, f D has one derivative in L p (D) of the boundary and the Neumann data is in L p (N). We find a p 0 > 1 so that for p in an interval (1, p 0), we may find(More)
We study the boundary regularity of solutions of the mixed problem for Laplace's equation in a Lipschitz graph domain Ω whose boundary is decomposed as ∂Ω = N ∪ D, where N ∩ D = ∅. For a subclass of these domains, we show that if the Neumann data g is in L p (N) and if the Dirichlet data f is in the Sobolev space L p,1 (D), for 1 < p < 2, then the mixed(More)
We consider the mixed boundary value problem, or Zaremba's problem for the Laplacian in a bounded Lipschitz domain Ω in R n , n ≥ 2. We decompose the boundary ∂Ω = D ∪ N with D and N disjoint. The boundary between D and N is assumed to be a Lipschitz surface in ∂Ω. We specify Dirichlet data on D in the Sobolev space W 1,p (D) and Neumann data in L p (N).(More)
We consider the mixed problem for the Lamé system              Lu = 0 in Ω u| D = f D on D ∂u ∂ρ = f N on N (∇u) * ∈ L p (∂Ω) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω and ∂/∂ρ stands for the traction operator. We suppose the Dirichlet data f D has one derivative in L p (D) and the traction data f N is in L p(More)