中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
非线性泛函分析研讨班
Speaker: 张泽鑫 博士（江苏大学）
Inviter: 张志涛
Language: Chinese
Title: Optimal uniform regularity of positive solutions to some elliptic systems with strong competition
Time & Venue: 2026年7月21日（星期二）11:00-12:00 南楼N818
Abstract: In this talk, we prove uniform interior and global Lipschitz bounds for positive solutions to strongly competing elliptic systems of either Gross-Pitaevskii type or Lotka-Volterra type, as the competition parameter tends to infinity. This bound is optimal, as the limiting profile is at most Lipschitz continuous by the Hopf lemma. In the Gross-Pitaevskii case, our uniform interior regularity result removes key assumptions required in previous works, and we further obtain global regularity. In the Lotka-Volterra case, we mainly consider the situation where the coupling coefficients are asymmetric and the competition terms are nonhomogeneous. The proof is based on blow-up analysis and Alt-Caffarelli-Friedman-type monotonicity formulae. This work is partially joint with Prof. Zhitao Zhang.
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