“…Blow up analysis for Moser-Trudinger functional is dealt in [19,25,26,36]. We list a few other related works in this direction [1,2,3,10,12,13,18,16,20,22,30,32,34] and the references there in for the available literatures in this direction.…”
Moser-Trudinger inequality was generalised by Calanchi-Ruf to the following version: If β ∈ [0, 1) and w 0 (x) = | log |x|| β(n−1) or log e |x| β(n−1)2010 Mathematics Subject Classification. Primary: 35B38, 35J20, 47N20, 26D10; Secondary: 46E35.
“…Blow up analysis for Moser-Trudinger functional is dealt in [19,25,26,36]. We list a few other related works in this direction [1,2,3,10,12,13,18,16,20,22,30,32,34] and the references there in for the available literatures in this direction.…”
Moser-Trudinger inequality was generalised by Calanchi-Ruf to the following version: If β ∈ [0, 1) and w 0 (x) = | log |x|| β(n−1) or log e |x| β(n−1)2010 Mathematics Subject Classification. Primary: 35B38, 35J20, 47N20, 26D10; Secondary: 46E35.
“…Moser-Trudinger type inequality had been an interesting topic of research for several authors. We list a few of them [1,2,3,7,8,13,10,12,14,15,18] and the references there in for the available literature in this direction.…”
On the space of weighted radial Sobolev space, the following generalization of MoserTrudinger type inequality was established by Calanchi and Ruf in dimension 2 : If β ∈ [0, 1) and w0(x) = | log |x||
“…N −1 and ω N −1 is the surface area of the unit ball in R N . Recently, the influence of weights on limiting inequalities of Trudinger-Moser type has been studied, for example, see [3,9,4,5,14,15]. If ω ∈ L 1 (Ω) is a non-negative function, we introduce the weighted Sobolev space…”
In this paper, we prove the existence of a nontrivial solution for the following boundary value problem −div ω(x)|∇u(x)| N −2 ∇u(x) = f (x, u), in B;
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