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arXiv · 1810.06319

Inverse problems for a fractional conductivity equation

Giovanni Covi
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Abstract

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 Schr\"odinger 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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Giovanni Covi. 2018-10-15. Inverse problems for a fractional conductivity equation. https://arxiv.org/abs/1810.06319

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