The Onsager-Machlup function, namely the fictitious density of diffusion paths in function space, is considered, where the density is evaluated around non $C^2$ curves, thus extending earlier results. The extension holds also for the case of diffusions evolving on a manifold.
"On the Onsager-Machlup Functional of Diffusion Processes Around Non $C^2$ Curves." Ann. Probab. 17 (3) 1037 - 1054, July, 1989. https://doi.org/10.1214/aop/1176991255