Extremal functions for singular Moser–Trudinger embeddings. (June 2017)

• Record Type: Journal Article
• Authors: Iula, Stefano; Mancini, Gabriele
• Is Part Of: Nonlinear analysis. Volume 156(2017)
• Page Start: 215
• Page End: 248
• Publication Date: 2017-06
• Subjects: 35J15 -- 35J60 -- 35J75 -- 35B44 -- 58J05; Moser–Trudinger -- Extremal functions -- Conical singularities; 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.2017.02.029
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study Moser–Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson–Chang type estimate by means of Onofri's inequality for the unit disk in R 2 . Moreover we extend the analysis of Adimurthi (2004) and Csató and Roy (2015a) considering Adimurthi–Druet type functionals on compact surfaces with conical singularities and discussing the existence of extremals for such functionals.