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arXiv · 1810.12329

On a weighted Trudinger-Moser inequality in $\mathbb{R}^N$

Emerson Abreu·Leandro G. Fernandes Jr
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Abstract

We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type $\displaystyle Lu:=-r^{-θ}(r^α\vert u'(r)\vert^βu'(r))'$, where $θ, β\geq 0$ and $α>0$, are constants satisfying some existence conditions. It worth emphasizing that these operators generalize the $p$- Laplacian and $k$-Hessian operators in the radial case. Our results involve fractional dimensions, a new weighted Pólya-Szeg{ö} principle, and a boundness value for the optimal constant in a Gagliardo-Nirenberg type inequality.

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Emerson Abreu, Leandro G. Fernandes Jr. 2018-10-29. On a weighted Trudinger-Moser inequality in $\mathbb{R}^N$. https://arxiv.org/abs/1810.12329

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