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Main Authors: Borthwick, Jack, Kamran, Niky
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.21944
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author Borthwick, Jack
Kamran, Niky
author_facet Borthwick, Jack
Kamran, Niky
contents We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-Émery Laplacian $-Δ_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary $(\overline{M},g)$, endowed with a volume form $\mathfrak{m}=e^{-V}ω_g$. These consist in recovering the Taylor coefficients of metric $g$ and weight $V$ along the boundary of $\overline{M}$ from the knowledge of a pair of operators that can be viewed as geometrically natural Dirichlet-to-Neumann maps associated to $-Δ_{\mathcal E}$.
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institution arXiv
publishDate 2025
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spellingShingle Inverse problems for the Bakry-Émery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness
Borthwick, Jack
Kamran, Niky
Analysis of PDEs
We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-Émery Laplacian $-Δ_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary $(\overline{M},g)$, endowed with a volume form $\mathfrak{m}=e^{-V}ω_g$. These consist in recovering the Taylor coefficients of metric $g$ and weight $V$ along the boundary of $\overline{M}$ from the knowledge of a pair of operators that can be viewed as geometrically natural Dirichlet-to-Neumann maps associated to $-Δ_{\mathcal E}$.
title Inverse problems for the Bakry-Émery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness
topic Analysis of PDEs
url https://arxiv.org/abs/2503.21944