| Abstract: |
| We discuss some recent results on Trudinger-Moser type inequalities on the whole space $\mathbb R^N$ with an \it{increasing radial} weight, in the framework of Sobolev mass-weighted spaces.
The presence of an increasing weight prevents us us to use rearrangement arguments: we perform instead a suitable change of variable, which allow us to prove non sharp Trudinger-type inequalities and to determine the sharp Moser exponents.
We also address the problem of the corresponding sharp Moser type inequalities and related concentration/vanishing phenomena. |
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