Monotonicity and 1-dimensional symmetry for solutions of an elliptic system arising in Bose-Einstein condensation

DOI10.1007/s00205-014-0724-2zbMath1293.35293arXiv1303.1265OpenAlexW3099143186MaRDI QIDQ2453518

Nicola Soave, Alberto Farina

Publication date: 6 June 2014

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.1265

zbMATH Keywords

Bose-Einstein condensatesnonlinear Schrödinger equationsAllen-Cahn equationsemilinear elliptic systemGross-Pitaevskii equationsblow-down family

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum equilibrium statistical mechanics (general) (82B10) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)

Related Items (13)

On the uniqueness of solutions of a nonlocal elliptic system ⋮ Some monotonicity results for general systems of nonlinear elliptic PDEs ⋮ Gradient Lagrangian systems and semilinear PDE ⋮ Solutions of multi-component fractional symmetric systems ⋮ Stable solutions of symmetric systems on Riemannian manifolds ⋮ On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition ⋮ Symmetry and asymmetry of components for elliptic Gross-Pitaevskii system ⋮ Monotonicity and rigidity of solutions to some elliptic systems with uniform limits ⋮ Uniform bounds for strongly competing systems: the optimal Lipschitz case ⋮ On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects ⋮ Moving planes for domain walls in a coupled system ⋮ Liouville theorems and 1-dimensional symmetry for solutions of an elliptic system modelling phase separation ⋮ On the De Giorgi Type Conjecture for an Elliptic System Modeling Phase Separation

Cites Work

• Unnamed Item
• Unnamed Item
• On entire solutions of an elliptic system modeling phase separations
• The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture
• Regularity of the nodal set of segregated critical configurations under a weak reflection law
• Positive solutions for a weakly coupled nonlinear Schrödinger system
• Bound states for a coupled Schrödinger system
• Multiple bound states of nonlinear Schrödinger systems
• Radial solutions and phase separation in a system of two coupled Schrödinger equations
• Multipulse phases in k-mixtures of Bose-Einstein condensates
• Elliptic partial differential equations of second order
• Symmetry for solutions of semilinear elliptic equations in \(\mathbb{R}^N\) and related conjectures
• On phase-separation models: asymptotics and qualitative properties
• A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
• Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
• Asymptotic estimates for the spatial segregation of competitive systems
• Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
• On the De Giorgi Type Conjecture for an Elliptic System Modeling Phase Separation
• Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition
• Standing waves of some coupled nonlinear Schrödinger equations
• Entire solutions with exponential growth for an elliptic system modelling phase separation
• Asymptotic behaviour of solutions of planar elliptic systems with strong competition

This page was built for publication: Monotonicity and 1-dimensional symmetry for solutions of an elliptic system arising in Bose-Einstein condensation