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arXiv · 2608.17797

The Calderón problem for the infinity Laplacian with large affine boundary data

Yi-Hsuan Lin
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Abstract

We study the Calderón problem for the equation $-Δ_\infty u+q(x)u=0$ in a bounded convex domain with $C^2$ boundary. We prove that a positive potential $q$ is uniquely determined and explicitly reconstructible from the measurements $Λ_q\bigl(t(e\cdot x+b)|_{\partialΩ}\bigr)$, where $e\in\mathbb S^{n-1}$, the offset $b>\sup_{\overlineΩ}|x|$ is fixed, and $t\to\infty$. The first potential-dependent term in the large amplitude asymptotics determines weighted integrals of $q$ over the chords parallel to $e$. Combining the measurements in the directions $e$ and $-e$ gives the X-ray transform of the zero extension of $q$, and the Fourier slice identity yields reconstruction and uniqueness.

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Yi-Hsuan Lin. 2026-08-18. The Calderón problem for the infinity Laplacian with large affine boundary data. https://arxiv.org/abs/2608.17797

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