caa a22 4500 475805291 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/s003329910014 doi (NATIONALLICENCE)springer-10.1007/s003329910014 Singular Perturbation and the Energy of Folds [Elektronische Daten] [W. Jin, R. V. Kohn] $\int \epsilon^{-1} (1-|\nabla u|^2)^2 + \epsilon |\nabla \nabla u|^2$ : 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 . Springer-Verlag New York Inc., 2000 Key words. singular perturbation, gamma—convergence, lower bounds, fold energy, viscosity solution, transition layers nationallicence Jin W. Department of Mathematics, Indiana University, Bloomington, IN 47405, USA wejin@indiana.edu, US aut Kohn R. V. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA kohn@cims.nyu.edu, US aut Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 355-390 0938-8974 10:3<355 2000 10 332 https://doi.org/10.1007/s003329910014 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003329910014 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jin W. Department of Mathematics, Indiana University, Bloomington, IN 47405, USA wejin@indiana.edu, US aut NATIONALLICENCE 700 1- Kohn R. V. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA kohn@cims.nyu.edu, US aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 355-390 0938-8974 10:3<355 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer