论文标题
相对于谐波功能，非线性边界价值问题
Nonlinear boundary value problems relative to harmonic functions
论文作者
论文摘要
我们研究找到u验证功能的问题 - $δ$ u = 0 in $ω$在$ \ partial $ \ poartial $ u $ \ partial $ \ partial $ n + g（u）= $ n + g（u）= $ \ partial $ \ partial $ \ partial $ partial $ partial $ there $ \ $ω$ $ $ $ $ \子集$ r n是$ $ $ $ $ $ $ g $ us $ $ gus $ us $ us的$μ连续无抵押函数。我们在G上给出了足够的条件，以便任何措施都可以解决此问题。当g（r）= | r | p - 1 r，p> 1，我们提供条件，以便可移动$ \ partial $$ω$上的孤立奇异性。我们还以$μ$ $ $的量度给出了电容性条件，以便与g（r）= | r |的问题。 p - 1 r可解决一些$μ$。我们还研究了满足函数的孤立奇点-UD $δ$ u = 0 in $ω$和$ \ partial $ u $ \ partial $ n + g（u）= 0 on $ \ partial $ \ partial $$ω$ \ {0}。
We study the problem of finding a function u verifying --$Δ$u = 0 in $Ω$ under the boundary condition $\partial$u $\partial$n + g(u) = $μ$ on $\partial$$Ω$ where $Ω$ $\subset$ R N is a smooth domain, n the normal unit outward vector to $Ω$, $μ$ is a measure on $\partial$$Ω$ and g a continuous nondecreasing function. We give sufficient condition on g for this problem to be solvable for any measure. When g(r) = |r| p--1 r, p > 1, we give conditions in order an isolated singularity on $\partial$$Ω$ be removable. We also give capacitary conditions on a measure $μ$ in order the problem with g(r) = |r| p--1 r to be solvable for some $μ$. We also study the isolated singularities of functions satisfying --$Δ$u = 0 in $Ω$ and $\partial$u $\partial$n + g(u) = 0 on $\partial$$Ω$ \ {0}.
