论文标题
椭圆形汉密尔顿 - 雅各比系统和车道填充hardy-h {é}非方程式
Elliptic Hamilton-Jacobi systems and Lane-Emden Hardy-H{é}non equations
论文作者
论文摘要
在这里，我们研究系统的任何迹象的解决方案 - $δ$ u 1 = | $ \ nabla $ u 2 | p， - $δ$ u 2 = | $ \ nabla $ u 1 | q，在r n，n 3和p，q> 0的域中，pq> 1 ..我们显示了它们与巷零件hardy-h {é}非方程式的关系 - $δ$ n p w = $ n p w = $ n p w = $ h $ r $ p $ f $ f $ f $ q q，$ε$ = $ = $ \ $ \ pm $ $ $ $ $ $ $ \ rightarrow $ \ rightarrow $ $ $ n p u n p u n p u> p> p> p> p> p> p> p> p> p> p> p> p， 1和$σ$ $ \ in $R。这导致我们在不经常处理参数n，p，$σ$的范围内探索这些方程。我们对系统和Hardy-Henon方程的径向解决方案进行了完整描述，并为非放射线提供了先验估计和Liouville类型的结果。
Here we study the solutions of any sign of the system --$Δ$u 1 = |$\nabla$u 2 | p , --$Δ$u 2 = |$\nabla$u 1 | q , in a domain of R N , N 3 and p, q > 0, pq > 1.. We show their relation with Lane-Emden Hardy-H{é}non equations --$Δ$ N p w= $ε$r $σ$ w q , $ε$ = $\pm$1, where u $\rightarrow$ $Δ$ N p u (p > 1) is the p-Laplacian in dimension N, q > p -- 1 and $σ$ $\in$ R. This leads us to explore these equations in not often tackled ranges of the parameters N, p, $σ$. We make a complete description of the radial solutions of the system and of the Hardy-Henon equations and give nonradial a priori estimates and Liouville type results.
