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.
Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer–Yan spikes revisited
Jevnikar A.;
2026-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
