退化散度型方程Perron方法的分辨性和不变性
Resolutivity and invariance for the Perron method for degenerate equations of divergence type
摘要：
考虑拟线性椭圆型方程$\mathop{\rm div}\mathcal{A}(x,\nabla u) = 0$在有界开集$Ω\subset\mathbf{R}^n$上狄利克雷问题的Perron解.向量值函数$\mathcal{A}$满足具有参数$1<p<\infty$和$p$ -容许权重$w$的标准椭圆率假设。我们表明，任意扰动集的$(p,w)$ -容量为零的连续（和某些准连续）的边界数据$f$是可分辨的和Perron解决方案的$f$和这样的扰动相吻合。因此，我们证明了Perron解决方案与连续的边界数据是唯一的有界的解决方案，所需的边界数据以外的一组$(p,w)$ -容量为零。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
