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RESEARCH PRODUCT

Inverse problems for a fractional conductivity equation

Giovanni Covi

subject

fractional conductivity equationosittaisdifferentiaaliyhtälötMathematics - Analysis of PDEsnon-local operatorscalderón problemFOS: Mathematicsinversio-ongelmatAnalysis of PDEs (math.AP)35R11 35R30

description

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.

yearjournalcountryeditionlanguage
2020-01-01Nonlinear Analysis
10.1016/j.na.2019.01.008http://dx.doi.org/10.1016/j.na.2019.01.008