具有大仿射边界数据的无穷拉普拉斯方程的卡尔德隆问题
The Calderón problem for the infinity Laplacian with large affine boundary data
AI总结：
该研究针对带大仿射边界数据的无穷拉普拉斯方程的卡尔德隆问题，通过特定边界测量值结合傅里叶切片定理，实现了正势的唯一确定与显式重构。
AI中文摘要：
我们研究在具有C²边界的有界凸区域内，方程-Δ_∞ u + q(x)u = 0的卡尔德隆问题。我们证明：正势q可从测量值Λ_q(t(e·x + b)|_{∂Ω})中唯一确定且可显式重构，其中e∈ℝ^{n-1}，偏移量b>sup_{Ω̄}|x|为固定值，t→∞。大振幅渐近中第一个依赖势的项确定了q在平行于e的弦上的加权积分。结合方向e与-e的测量值可得到q零延拓的X射线变换，而傅里叶切片定理可实现重构与唯一性。
英文摘要：
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.
