Non-Linear Effects in a Yamabe-Type Problem with Quasi-Linear Weight

Details Non-Linear Effects in a Yamabe-Type Problem with Quasi-Linear Weight Non-Linear Effects in a Yamabe-Type Problem with Quasi-Linear Weight

2011-01-07

arxiv.org/abs/1101.1462v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

We study the quasi-linear minimization problem on $H^1_0(\Omega)\subset L^q$
with $q=\frac{2n}{n-2}$~: $$\inf_{\|u\|_{L^q}=1}\int_\Omega (1+|x|^\beta
|u|^k)|\nabla u|^2.$$ We show that minimizers exist only in the range
$\betathe linear influence for $\beta\geq kn/q$ prevents their existence.

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