TY - JOUR
T1 - Classification of singular limits for free boundary and singularly perturbed elliptic problems
T2 - the Dancer–Yan spikes revisited
AU - Bartolucci, Daniele
AU - Jevnikar, Aleks
AU - Wei, Juncheng
AU - Wu, Ruijun
N1 - Publisher Copyright:
© The Author(s) 2026. Published by Oxford University Press. All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/pages/standard-publication-reuse-rights)
PY - 2026/9
Y1 - 2026/9
N2 - We classify the singular limits relative to a free boundary problem arising in plasma physics in dimension (Formula presented), under suitable natural integral bounds. It turns out that one of the asymptotic behaviors corresponds to the Dancer–Yan spikes (J. London Math. Soc. (78) 2008, 639–662). Interestingly enough, in the more general setting where we drop boundary conditions, and in striking contrast with the higher dimensional case, the spiking structure becomes more rich, including profiles that are not Dancer–Yan spikes. We succeed in a detailed description of the singular limits by a careful analysis, from local to global, of the tiny difference between the maximum value of the spikes and their “vanishing level” defining the free boundary.
AB - We classify the singular limits relative to a free boundary problem arising in plasma physics in dimension (Formula presented), under suitable natural integral bounds. It turns out that one of the asymptotic behaviors corresponds to the Dancer–Yan spikes (J. London Math. Soc. (78) 2008, 639–662). Interestingly enough, in the more general setting where we drop boundary conditions, and in striking contrast with the higher dimensional case, the spiking structure becomes more rich, including profiles that are not Dancer–Yan spikes. We succeed in a detailed description of the singular limits by a careful analysis, from local to global, of the tiny difference between the maximum value of the spikes and their “vanishing level” defining the free boundary.
UR - https://www.scopus.com/pages/publications/105048244171
U2 - 10.1093/imrn/rnag187
DO - 10.1093/imrn/rnag187
M3 - Article
AN - SCOPUS:105048244171
SN - 1073-7928
VL - 2026
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 17
M1 - rnag187
ER -