Trudinger–Moser type inequalities with a symmetric conical metric and a symmetric potential. (October 2022)

• Record Type: Journal Article
• Authors: de Souza, Manassés X.
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: primary 58J05 -- secondary 35B44; Trudinger–Moser inequality -- Blow-up analysis -- Conical singularity; 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.2022.113030
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let ( M, g ) be a closed Riemann surface, where the metric g has certain conical singularities at finite points. Suppose Γ is a group with elements of isometries acting on ( M, g ) . In this paper, Trudinger–Moser inequalities involving Γ and the operador Δ g + V are established, where Δ g denotes the Laplace–Beltrami operator associated to g and the potential V : M → ( 0, ∞ ) belongs to a class of symmetric and continuous functions. Moreover, via the method of blow-up analysis, the corresponding extremals are also obtained.