论文标题
$ 1 $ -LAPLACIAN的DIRICHLET问题，具有一般性的单词和$ L^1 $ -DATA
The Dirichlet problem for the $1$-Laplacian with a general singular term and $L^1$-data
论文作者
论文摘要
我们研究了一个椭圆方程的差异问题，涉及$ 1 $ - laplace操作员和一个反应术语，即：$$ \ left \ webt {array} {array} {ll} {ll} \ displayStyle -uplayStyle-Δ_1u = h（x）＆\ hbox {in} } \partialΩ\ ,, \ end {array} \ right。 $$其中$ω\ subset \ mathbb {r}^n $是具有Lipschitz边界的开放式集合，$ f \ in l^1（ω）$是非负的，而$ h $是一个连续的真实功能，可能在零时可能会爆炸。我们研究了数据的最佳范围，以获得非负溶液的存在，不存在和（任何预期）唯一性。
We study the Dirichlet problem for an elliptic equation involving the $1$-Laplace operator and a reaction term, namely: $$ \left\{\begin{array}{ll} \displaystyle -Δ_1 u =h(u)f(x)&\hbox{in }Ω\,,\\ u=0&\hbox{on }\partialΩ\,, \end{array}\right. $$ where $ Ω\subset \mathbb{R}^N$ is an open bounded set having Lipschitz boundary, $f\in L^1(Ω)$ is nonnegative, and $h$ is a continuous real function that may possibly blow up at zero. We investigate optimal ranges for the data in order to obtain existence, nonexistence and (whenever expected) uniqueness of nonnegative solutions.
