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Abstract
This work considers properties of the logarithm of the NeumanntoDirichlet boundary map for the conductivity equation in a Lipschitz domain. It is shown that the mapping from the (logarithm of) the conductivity, i.e., the (logarithm of) the coefficient in the divergence term of the studied elliptic partial differential equation, to the logarithm of the NeumanntoDirichlet map is continuously Frechet differentiable between natural topologies. Moreover, for any essentially bounded perturbation of the conductivity, the Frechet derivative defines a bounded linear operator on the space of square integrable functions living on the domain boundary, although the logarithm of the NeumanntoDirichlet map itself is unbounded in that topology. In particular, it follows from the fundamental theorem of calculus that the difference between the logarithms of any two Neumannto Dirichlet maps is always bounded on the space of square integrable functions. All aforementioned results also hold if the NeumanntoDirichlet boundary map is replaced by its inverse, i.e., the DirichlettoNeumann map.
Original language  English 

Pages (fromto)  197–220 
Number of pages  24 
Journal  SIAM Journal on Mathematical Analysis 
Volume  52 
Issue number  1 
DOIs  
Publication status  Published  9 Jan 2020 
MoE publication type  A1 Journal articlerefereed 
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Dive into the research topics of 'On regularity of the logarithmic forward map of electrical impedance tomography'. Together they form a unique fingerprint.Projects
 1 Finished

Centre of Excellence of Inverse Modelling and Imaging
Hyvönen, N., Hirvi, P., Kuutela, T., Ojalammi, A., Perkkiö, L. & Puska, J.
01/01/2018 → 31/12/2020
Project: Academy of Finland: Other research funding