Simetria de extremais para desigualdades de Trudinger-Moser com peso do tipo Hénon

Abstract

In this work, we will study the existence, symmetry and asymptotic behavior of the extremal functions of the problem S( ; ) = supu2H1()kuk 1Z(e u2􀀀 1)jxjdx; (1)]where is the unit ball of R2, ; > 0.We will show symmetry properties as ! 1 and ! 0. We will also study, due to its influence on the problem (1), the symmetry and asymptotic behavior, as ! 0, of the extremal functions for the Trudinger-Moser trace inequality, that is,T( ) = supu2H1()kuk 1Z@ (e u2􀀀 1)d : (2)