论文标题
Perron方法的分辨率和不变性，用于变化类型的退化方程
Resolutivity and invariance for the Perron method for degenerate equations of divergence type
论文作者
论文摘要
我们考虑了quasilinear椭圆方程的dirichlet问题的解决方案$ \ mathop {\ rm div} \ mathcal {a}（x，x，x，\ nabla u）= 0 $ = 0 $ in BOINDED OPEN SET SET $ω\ subset \ subset \ subset \ mathbf {r}^n $。矢量值函数$ \ MATHCAL {a} $以参数为$ 1 <p <\ infty $和a $ p $ - 加热的权重$ w $的标准椭圆形假设。我们表明，$（p，w）$ - 连续（和某些难度）边界数据$ f $的零容量的任意扰动是零的，并且$ f $的perron解决方案以及这种扰动重合。结果，我们证明具有连续边界数据的PERRON解决方案是独特的有界解决方案，它将所需的边界数据放置在一组$（p，w）$ - 容量零之外。
We consider Perron solutions to the Dirichlet problem for the quasilinear elliptic equation $\mathop{\rm div}\mathcal{A}(x,\nabla u) = 0$ in a bounded open set $Ω\subset\mathbf{R}^n$. The vector-valued function $\mathcal{A}$ satisfies the standard ellipticity assumptions with a parameter $1<p<\infty$ and a $p$-admissible weight $w$. We show that arbitrary perturbations on sets of $(p,w)$-capacity zero of continuous (and certain quasicontinuous) boundary data $f$ are resolutive and that the Perron solutions for $f$ and such perturbations coincide. As a consequence, we prove that the Perron solution with continuous boundary data is the unique bounded solution that takes the required boundary data outside a set of $(p,w)$-capacity zero.
