论文标题
某些完全非线性单数或退化方程的存在和规律性结果
Existence and regularity results for some Fully Non Linear singular or degenerate equation
论文作者
论文摘要
在本文中，我们证明了单数方程的存在，独特性和规律性\ begin {eqnarray*} \ begin {case} | \ nabla u |^α（f（d^{2} u） } \ Ω\\ u>0 \ \mbox{ in } \ Ω, \ u=0 \ \mbox{ on } \ \partialΩ\end{cases} \end{eqnarray*} when $p$ is some continuous and positive function, $c$ and $h$ are continuous, $α> -1$ and $F$ is Fully non linear elliptic.需要运算符的第一个特征值$ | \ nabla u |^α（f（d^{2} u）+h（x）\ cdot \ nabla u）+c（x）| u |^αu$。结果概括了Lazer和Mac Kenna的众所周知的结果。
In this article we prove existence, uniqueness and regularity for the singular equation \begin{eqnarray*} \begin{cases} |\nabla u|^α(F(D^{2}u)+h(x)\cdot\nabla u)+c(x)|u|^αu+p(x)u^{-γ}=0 \ \mbox{ in } \ Ω\\ u>0 \ \mbox{ in } \ Ω, \ u=0 \ \mbox{ on } \ \partialΩ\end{cases} \end{eqnarray*} when $p$ is some continuous and positive function, $c$ and $h$ are continuous, $α> -1$ and $F$ is Fully non linear elliptic. Some conditions on the first eigenvalue for the operator $|\nabla u|^α(F(D^{2}u)+h(x)\cdot\nabla u)+c(x)|u|^αu$ are required. The results generalizes the well known results of Lazer and Mac Kenna.
