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arXiv · 1405.7734

The effects of a discontinues weight for a problem with a critical nonlinearity

Rejeb Hadiji·Sami Baraket·Yabib Yazidi
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Abstract

We study the minimizing problem $\inf\left\{\displaystyle\int_{\Omega}p(x)|\nabla u|^{2}dx,\,u\in H^{1}_{0}(\Omega),\,\|u\|_{L^{\frac{2N}{N-2}}(\Omega)}=1\right\}$ where $\Omega$ is a smooth bounded domain of $\R^{N}$, $N\geq 3$ and $p$ a positive discontinuous function. We prove the existence of a minimizer under some assumptions.

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Rejeb Hadiji, Sami Baraket, Yabib Yazidi. 2014-05-29. The effects of a discontinues weight for a problem with a critical nonlinearity. https://arxiv.org/abs/1405.7734

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