Determination of the potential by a fixed angle scattering data

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This is a Quantitative Study study.

Suliang Si

doi:10.48550/arxiv.2506.21251

June 26, 2025Open Access

Determination of the potential by a fixed angle scattering data

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Key Points

A compactly supported potential is uniquely identified by fixed angle scattering data, emphasizing its importance in mathematical physics.
The study reveals that using a new Carleman estimate significantly enhances the solution approach for potential determination.
Building on Bukhgeim and Klibanov's concepts, this method for inverse problems proves the efficacy of Carleman estimates.
These findings have implications for further research in mathematical theories involving scattering data applications.

Implication

This analysis shows a unique relationship between a potential and scattering results, suggesting new methods for inverse problems.

Abstract

In this paper, we show that a compactly supported potential is uniquely determined by the far field pattern at a fixed angle. Our method is based on a new Carleman estimate and the ideas introduced by Bukhgeim and Klibanov on the use of Carleman estimates for inverse problems.

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Cite This Study

Suliang Si (2025) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06e7c5 https://doi.org/10.48550/arxiv.2506.21251

View Full Paper

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Determination of the potential by a fixed angle scattering data

Key Points

Implication

Abstract

Discussion

Cite This Study

Determination of the potential by a fixed angle scattering data

Key Points

Implication

Abstract

Discussion

Cite This Study

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