Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary. (December 2022)

• Record Type: Journal Article
• Authors: Almaraz, Sérgio; Wang, Shaodong
• Is Part Of: Nonlinear analysis. Volume 225(2022)
• Publication Date: 2022-12
• Subjects: Sign-changing solutions -- Energy bounds -- Yamabe equation -- Nonlinear boundary conditions; 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.2022.113131
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Yamabe equation in the Euclidean half-space. We prove that any sign-changing solution has at least twice the energy of a standard bubble. Moreover, a sharper energy lower bound of the sign-changing solution set is also established via the method of moving planes. This bound increases the energy range for which Palais–Smale sequences of related variational problem has a non-trivial weak limit.