On the behaviour of the solutions to p-Laplacian equations as p goes to 1
On the behaviour of the solutions to p-Laplacian equations as p goes to 1
复制标题
当 p 变为 1 时 p-拉普拉斯方程解的行为
DOI：
10.5565/publmat_52208_07
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发表时间：
2008
影响因子：
1.1
通讯作者：
C. Trombetti
中科院分区：
文献类型：
--
作者：
A. Mercaldo;S. S. D. León;C. Trombetti
本文研究了p到1的弱函数的行为
解决问题的方法
$$
\开始{cases}
-\operatorname{div} \bigl（|\nabla u_p| ^{p-2}\nabla u_p\bigr）=f
&\text{in } \Omega\\
u_p=0 &\text{on } \partial\Omega，
\end{cases}
$$
其中$\Omega$是${\martbb R}^N$ $（N\ge 2）$的有界开集，
Lipschitz边界和p > 1。如果$f$是
我们分析了几种情况：最一般的情况是$f\in
W^{-1，\infty}（\Omega）$.我们还说明了我们的结果，通过
评论和例子。
In the present paper we study the behaviour as $p$ goes to $1$ of the weak
solutions to the problems
$$
\begin{cases}
-\operatorname{div} \bigl(|\nabla u_p|^{p-2}\nabla u_p\bigr)=f
&\text{in } \Omega\\
u_p=0 &\text{on } \partial\Omega,
\end{cases}
$$
where $\Omega$ is a bounded open set of ${\mathbb R}^N$ $(N\ge 2)$ with
Lipschitz boundary and $p > 1$. As far as the datum $f$ is
concerned, we analyze several cases: the most general one is $f\in
W^{-1,\infty}(\Omega)$. We also illustrate our results by means of
remarks and examples.