Convergence of minimax structures and continuation of critical points for singularly perturbed systems

Noris, Benedetta, et al. "Convergence of minimax structures and continuation of critical points for singularly perturbed systems." Journal of the European Mathematical Society 014.4 (2012): 1245-1273. <http://eudml.org/doc/277528>.

@article{Noris2012,
abstract = {In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system $-\Delta u+u^3+\beta uv^2=\lambda u,-\Delta v + v^3 + \beta u^2v=\mu v, u, v \in H^1_0(\Omega ), \ u,v > 0$, as the interspecies scattering length $\beta $ goes to $+\infty $. For this system we consider the associated energy functionals $J_\{\beta \}, \beta \in (0, +\infty )$, with $L^2$-mass constraints, which limit $J_\{\infty \}$ (as $\beta \rightarrow +\infty $) is strongly irregular. For such functionals, we construct multiple critical points via a common minimax structure, and prove convergence of critical levels and optimal sets. Moreover we study the asymptotics of the critical points.},
author = {Noris, Benedetta, Tavares, Hugo, Terracini, Susanna, Verzini, Gianmaria},
journal = {Journal of the European Mathematical Society},
keywords = {strongly competing system; gamma-convergence; Krasnoselskii genus; strongly competing system; gamma-convergence; Krasnoselskii genus},
language = {eng},
number = {4},
pages = {1245-1273},
publisher = {European Mathematical Society Publishing House},
title = {Convergence of minimax structures and continuation of critical points for singularly perturbed systems},
url = {http://eudml.org/doc/277528},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Noris, Benedetta
AU - Tavares, Hugo
AU - Terracini, Susanna
AU - Verzini, Gianmaria
TI - Convergence of minimax structures and continuation of critical points for singularly perturbed systems
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 4
SP - 1245
EP - 1273
AB - In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system $-\Delta u+u^3+\beta uv^2=\lambda u,-\Delta v + v^3 + \beta u^2v=\mu v, u, v \in H^1_0(\Omega ), \ u,v > 0$, as the interspecies scattering length $\beta $ goes to $+\infty $. For this system we consider the associated energy functionals $J_{\beta }, \beta \in (0, +\infty )$, with $L^2$-mass constraints, which limit $J_{\infty }$ (as $\beta \rightarrow +\infty $) is strongly irregular. For such functionals, we construct multiple critical points via a common minimax structure, and prove convergence of critical levels and optimal sets. Moreover we study the asymptotics of the critical points.
LA - eng
KW - strongly competing system; gamma-convergence; Krasnoselskii genus; strongly competing system; gamma-convergence; Krasnoselskii genus
UR - http://eudml.org/doc/277528
ER -