Revisiting the Lavrentiev phenomenon in one dimension
Volume 180 / 2026
Colloquium Mathematicum 180 (2026), 165-186
MSC: Primary 49-02; Secondary 49J30, 49J45
DOI: 10.4064/cm9527-11-2025
Published online: 14 April 2026
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.
