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

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 نشر من قبل Emerson Abreu
 تاريخ النشر 2018
  مجال البحث
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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 $displaystyle Lu:=-r^{-theta}(r^{alpha}vert u(r)vert^{beta}u(r))$, where $theta, betageq 0$ and $alpha>0$, 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 Polya-Szeg{o} principle, and a boundness value for the optimal constant in a Gagliardo-Nirenberg type inequality.



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