论文标题
一类准线性方程的阳性解决方案的痕量和边界奇异性
Trace and boundary singularities of positive solutions of a class of quasilinear equations
论文作者
论文摘要
我们研究满足正功能的属性 - $δ$ u+m | $ \ nabla $ u |问 - u p = 0是域$ω$或r n +中的p> 1和1 <q <2时。我们给出了足够的条件，即以（e）为边界数据的（e）的解决方案，并且这些条件以边界上的贝塞尔（Bessel）能力表示。我们还在$ \ partial $$ω$上使用孤立的奇异性研究可移动的边界奇点和解决方案。不同的结果取决于P = P C：= N +1 N -1的两个关键指数，以及Q = Q C：= N +1 N以及相对于2P P +1的Q位置。内容
We study properties of positive functions satisfying (E) --$Δ$u+m|$\nabla$u| q -- u p = 0 is a domain $Ω$ or in R N + when p > 1 and 1 < q < 2. We give sufficient conditions for the existence of a solution to (E) with a nonnegative measure $μ$ as boundary data, and these conditions are expressed in terms of Bessel capacities on the boundary. We also study removable boundary singularities and solutions with an isolated singularity on $\partial$$Ω$. The different results depends on two critical exponents for p = p c := N +1 N --1 and for q = q c := N +1 N and on the position of q with respect to 2p p+1. Contents
