Inverse problems for a fractional conductivity equation
Covi, G. (2020). Inverse problems for a fractional conductivity equation. Nonlinear Analysis: Theory, Methods and Applications, 193, 111418. https://doi.org/10.1016/j.na.2019.01.008
Published inNonlinear Analysis: Theory, Methods and Applications
©2019 The Author(s)
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schrödinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights.
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Related funder(s)European Commission
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingThis work is part of the PhD research of the author. The author was partially supported by the European Research Council under Horizon 2020 (ERC CoG 770924). The author wishes to dearly thank professor M. Salo for his precious ideas and helpful discussion in the making of this work.
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