Let Omega subsetR^N be a bounded smooth domain. We investigate theudeffect of the mean curvature of the boundary partial Omega on the behaviour of theudsolution to the homogeneous Dirichlet boundary value problem for the equationudDelta u + f(u) = 0. Under appropriate growth conditions on f(t) as t approachesudzero, we find asymptotic expansions up to the second order of the solution inudterms of the distance from x to the boundary partial Omega.
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机译：令 Omega subsetR ^ N为有界平滑域。我们研究边界部分 Omega的平均曲率对方程 ud Delta u + f（u）= 0的齐次Dirichlet边值问题的 udsolution行为的影响。在适当的增长条件下在f（t）上，当t接近 udzero时，我们发现在x到边界 partial Omega的距离的 uterms中，渐近展开直至解的二阶。
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