Unique determination of a Kato class potential from boundary data

We prove that a Kato class potential $V$ defined on an open, bounded set in $\mathbb{R}^3$ with Lipschitz boundary is uniquely determined by the Dirichlet-to-Neumann operator associated to the equation $-\Delta u + Vu = 0\,.$

Publication Details

Journal
ArXiv.org
Published
2025-02-21
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

Unique determination of a Kato class potential from boundary data

ArXiv.org
Nonlinear Partial Differential Equations
article

Unique determination of a Kato class potential from boundary data

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Abstract

We prove that a Kato class potential $V$ defined on an open, bounded set in $\mathbb{R}^3$ with Lipschitz boundary is uniquely determined by the Dirichlet-to-Neumann operator associated to the equation $-\Delta u + Vu = 0\,.$

ArXiv.org
Openalex Percentile: Top 39%
Nonlinear Partial Differential Equations
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Unique determination of a Kato class potential from boundary data · ArXiv.org (2025) | TGRS Research Map | TGRS