Determining coefficients for a fractional \(p\)-Laplace equation from exterior measurements (Q6595385)

The authors consider the inverse problem of recovering the weight function in a weighted, fractional \(p\)-Laplacian, which could also be called the fractional \(p\)-conductivity equation. The argument is based on focusing energy at a given point by using particular exterior data, supposing the weight function is sufficiently continuous. This also gives a stability result and, for real analytic weight functions, a global uniqueness result, generalizing in particular the result in [\textit{G. Covi} et al., ``The global inverse fractional conductivity problem'', Preprint, \url{arXiv:2204.04325}]. The method resembles the method of \textit{R. V. Kohn} and \textit{M. Vogelius} [Commun. Pure Appl. Math. 37, 289--298 (1984; Zbl 0586.35089)].