Moser functions and fractional Moser–Trudinger type inequalities. (November 2016)

• Record Type: Journal Article
• Authors: Hyder, Ali
• Is Part Of: Nonlinear analysis. Volume 146(2016)
• Page Start: 185
• Page End: 210
• Publication Date: 2016-11
• Subjects: Fractional Moser–Trudinger inequalities -- Nonlocal equations; 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.2016.08.024
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We improve the sharpness of some fractional Moser–Trudinger type inequalities, particularly those studied by Lam–Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to the problem ( − Δ ) n 2 u = λ u e b u 2 in Ω, 0 < λ < λ 1, b > 0, with Dirichlet boundary condition, for any domain Ω in R n with finite measure. Here λ 1 is the first eigenvalue of ( − Δ ) n 2 on Ω .