$\int \epsilon^{-1} (1-|\nabla u|^2)^2 + \epsilon |\nabla \nabla u|^2$
in two space dimensions. We introduce a new scheme for proving lower bounds and show the bounds are asymptotically sharp for certain domains and boundary conditions. Our results support the conjecture, due to Aviles and Giga, that folds are one-dimensional, i.e., \nabla u varies mainly in the direction transverse to the fold. We also consider related problems obtained when (1-|\nabla u| 2 ) 2 is replaced by (1-δ 2 u x 2 - u y 2 ) 2 or (1-|\nabla u| 2 ) 2γ .
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received April 21, 1999; accepted August 18, 1999
Rights and permissions
About this article
Cite this article
Jin, W., Kohn, R. Singular Perturbation and the Energy of Folds. J. Nonlinear Sci. 10, 355–390 (2000). https://doi.org/10.1007/s003329910014
Published:
Issue Date:
DOI: https://doi.org/10.1007/s003329910014