Document Type
Poster
Publication Date
Summer 2024
Abstract
The calculus of variations is a field of mathematical analysis that provides methods for finding optimizing functions of functionals. This research investigated the Lavrentiev Phenomenon, an important problem in the calculus of variations, which occurs when there is a gap in the infimum of the functional as the space of admissible functions is restricted. Specifically, we examine functionals for which the infimum is strictly greater in the space of Lipschitz functions than in the space of continuous and integrable functions. This poster introduces the classical example of a Lavrentiev Gap and proposes a generalization of this example. The research also includes a translation from French to English of M. Lavrentiev’s seminal 1926 paper, “Sur Quelques Problèmes du Calcul des Variations.”
Recommended Citation
Leblanc, Christophe and Snipes, Marie, "Investigating the Lavrentiev Phenomenon" (2024). Kenyon Summer Science Scholars Program. Paper 728.
https://digital.kenyon.edu/summerscienceprogram/728