Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities

2020/05/14 by Lin, Yi-Hsuan · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.07163

Abstract

We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and the derivative of the Dirichlet-to-Neumann map hold. Based on the strong monotonicity relations, we study a constructive global uniqueness for coefficients and inclusion detection for the fractional Calderón type inverse problem. Meanwhile, we can also derive the Lipschitz stability with finitely many measurements. The results hold for any n≥ 1.

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• Monotonicity and local uniqueness for an isotropic nonlocal elliptic equation
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