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We consider an inverse problem of determining the coefficients of afractional $p\,$-Laplace equation in the exterior domain. Assuming suitablelocal regularity of the coefficients in the exterior domain, we offer anexplicit reconstruction formula in the region where the exterior measurementsare performed. This formula is then used to establish a global uniquenessresult for real-analytic coefficents. In addition, we also derive a stabilityestimate for the unique determination of the coefficients in the exteriormeasurement set.

Determining coefficients for a fractional $p$-Laplace equation from exterior measurements