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arXiv · 1001.2063

Regularity of the extremal solution for a fourth-order elliptic problem with singular nonlinearity

Baishun Lai·Qing Luo
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Abstract

In this paper, we consider the relation between $p > 1$ and critical dimension of the extremal solution of the semilinear equation $$\{\begin{array}{lllllll} βΔ^{2}u-τΔu=\fracλ{(1-u)^{p}} & in\ \ B, 0 0$ is a parameter, $τ>0, β>0,p>1$ are fixed constants. By Hardy-Rellich inequality, we find that when $p$ is large enough, the critical dimension is 13.}

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Baishun Lai, Qing Luo. 2010-10-28. Regularity of the extremal solution for a fourth-order elliptic problem with singular nonlinearity. https://arxiv.org/abs/1001.2063

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