Moser functions and fractional Moser–Trudinger type inequalities. (November 2016) - Hyder, Ali
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 .