Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights
Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights
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DOI：
10.3934/cpaa.2004.3.653
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发表时间：
2004-09
影响因子：
1
通讯作者：
M. Chuaqui;C. Cortázar;M. Elgueta;J. García-Melián
中科院分区：
文献类型：
--
作者：
M. Chuaqui;C. Cortázar;M. Elgueta;J. García-Melián
考虑光滑有界域$\Omega$上的椭圆型问题$\Delta u=a(x)u^m$、$m>1$和$\Delta u=a(x)e^u$，在$\partial\Omega$上边界条件为$u=+\infty$。假设权函数$a(x)$是Holder连续的，在$\partial\Omega$附近像$d(x)=$ dist $(x,\partial\Omega)$的负幂一样增长。我们给出了解及其正规导数在边界附近的存在性和不存在性结果、唯一性和渐近估计。
We consider the elliptic problems $\Delta u=a(x)u^m$, $m>1$, and $\Delta u=a(x)e^u$ in a smooth bounded domain $\Omega$, with the boundary condition $u=+\infty$ on $\partial\Omega$. The weight function $a(x)$ is assumed to be Holder continuous, growing like a negative power of $d(x)=$ dist $(x,\partial\Omega)$ near $\partial\Omega$. We show existence and nonexistence results, uniqueness and asymptotic estimates near the boundary for both the solutions and their normal derivatives.