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

Manas Kar; Philipp Zimmermann; Yi-Hsuan Lin

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

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arxiv 2212.03057 v1 pith:SZSBFP3B submitted 2022-12-06 math.AP

Manas Kar , Yi-Hsuan Lin , Philipp Zimmermann This is my paper · ORCID

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keywords exteriorcoefficientsdeterminingdomainequationformulafractionallaplace

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abstract

We consider an inverse problem of determining the coefficients of a fractional $p\,$-Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients in the exterior domain, we offer an explicit reconstruction formula in the region where the exterior measurements are performed. This formula is then used to establish a global uniqueness result for real-analytic coefficents. In addition, we also derive a stability estimate for the unique determination of the coefficients in the exterior measurement set.

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An Inverse Obstacle Problem for the Fractional Schr\"odinger Equation
math.AP 2026-07 accept novelty 6.0 of 10

A countable family of scaled exterior measurements of the fractional Schrödinger obstacle problem determines the nonnegative potential throughout the domain.

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