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arXiv · 2411.16296

Revisiting the Lavrentiev Phenomenon in One Dimension

Wiktor Wichrowski
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Abstract

We clarify and extend insights from Lavrentiev's seminal paper. We examine the original theorem dealing with the absence of the Lavrentiev phenomenon, a cornerstone issue in the calculus of variations. We point out some inconsistencies in the original proof by providing a counterexample and supply the result with a new, concise, and complete reasoning. In the appendix, we also provide additional details to supplement the original proof.

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Wiktor Wichrowski. 2024-11-25. Revisiting the Lavrentiev Phenomenon in One Dimension. https://doi.org/10.4064/cm9527-11-2025

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