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- W2089528218 abstract "This paper studies the global uniqueness and stability questions of the inverselinebreak conductivity problem to determine the unknown object D entering $mbox{div}((1+(k-1)chi_D)nabla u)=0$linebreak in $Omega$ and $pd{u}{nu}=g$ on $partialOmega$ from the boundary measurement $Lambda_D(g)=u|_{bO}$. The results of this paperlinebreak are fourfold. We first obtain a Hölder stability estimate for disks. Second, a uniform stability estimate for the direct problem is obtained. Third, we obtain the stability estimates $|D_1 setminus bar D_2| +|D_2 setminus bar D_1| le C ( | Lambda_{D_1} (g) - Lambda_{D_2} (g) |_{L^infty(bO)}^{alpha} + ep )$ for some $alpha >0$ when g satisfies some condition if D1 and D2 are $ep$-perturbations of two disks. We then drop the condition on g and show that if $Lambda_{D_1} (g) = Lambda_{D_2} (g)$ on $bO$, then the two domains must be very close." @default.
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- W2089528218 date "1999-01-01" @default.
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- W2089528218 title "Inverse Conductivity Problem with One Measurement: Error Estimates and Approximate Identification for Perturbed Disks" @default.
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- W2089528218 doi "https://doi.org/10.1137/s0036141097324958" @default.
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