One-dimensional symmetry of solutions to non-cooperative elliptic systems. (February 2023)

• Record Type: Journal Article
• Authors: Le, Phuong
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: 35B06 -- 35B08 -- 35J47; Non-cooperative systems -- Gross–Pitaevskii system -- One-dimensional symmetry -- Domain walls -- Sliding method; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113156
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the monotonicity and one-dimensional symmetry of solutions to non-cooperative elliptic systems in R N with uniform limits under mild assumptions on the nonlinearities. These problems arise in the study of domain walls and interface layers of two-component Bose–Einstein condensates in the segregation regime. We also derive analogous results for systems in half-spaces and strips. We introduce a variant of the sliding method for non-cooperative elliptic systems to prove our results.