The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture

DOI10.1016/j.jfa.2011.10.013zbMath1242.35119OpenAlexW2107857844MaRDI QIDQ665516

Kelei Wang, E. Norman Dancer, Zhi-tao Zhang

Publication date: 5 March 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2011.10.013

zbMATH Keywords

singular perturbationpartial regularityfree boundary problemGross-Pitaevskii equationmonotonicity formula

Mathematics Subject Classification ID

Partial differential inequalities and systems of partial differential inequalities (35R45) Free boundary problems for PDEs (35R35) Second-order parabolic systems (35K40) Second-order elliptic systems (35J47)

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Cites Work

• Unnamed Item
• Unnamed Item
• Convergence of minimax structures and continuation of critical points for singularly perturbed systems
• Uniform Hölder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species
• Regularity of the nodal set of segregated critical configurations under a weak reflection law
• A geometric approach to the topological disk theorem of Reifenberg
• Some new results in competing systems with many species
• Nonlocal heat flows preserving the \(L^2\) energy
• A strong unique continuation theorem for parabolic equations
• Dynamics of Lotka-Volterra competition systems with large interaction
• Harmonic maps into singular spaces and \(p\)-adic superrigidity for lattices in groups of rank one
• On the Besicovitch property for parabolic balls
• The geometry of solutions to a segregation problem for nondivergence systems
• Asymptotic estimates for the spatial segregation of competitive systems
• Dynamics of strongly competing systems with many species
• Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition
• Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
• Doubling properties of caloric functions
• A variational problem for the spatial segregation of reaction-diffusion systems