Singular solutions of elliptic equations and the determination of conductivity by boundary measurements

Abstract We improve some results on uniqueness and stability in the determination of the coefficient a in the equation (i) div( a grad u ) = 0 in Ω, when all possible pairs of Dirichlet and Neumann data on ∂Ω are known. We also treat cases of anisotropic equations. Our method relies on the construction of solutions to (i) having an isolated singularity with prescribed asymptotic behaviour.

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