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

Benedetta Noris; Hugo Tavares; Susanna Terracini; Gianmaria Verzini

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 4, page 1245-1273
- ISSN: 1435-9855

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topNoris, 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 -

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