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

Yi Hsuan Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 derivatives 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.

Original languageEnglish
Article number188
JournalCalculus of Variations and Partial Differential Equations
Volume61
Issue number5
DOIs
StatePublished - Oct 2022

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