标题： 球面上的对称化及其应用 显示英文标题

标题： Symmetrization on the sphere and applications

摘要： 我们引入了一种映射在$n$-球面（$n\geq 2$）上的对称化新方法。 它们被用于估计带有右侧狄拉克测度组合的拟线性椭圆偏微分方程的解，这些方程属于$p$-拉普拉斯型。 当$p=n$时，通过共形变换将其简化为球面上的问题。 当$1 < p < n $和$p > $n 时的情况则更简略地进行讨论，详细内容见作者的其他论文。 显示英文摘要

摘要： We introduce a new method of symmetrization of mappings on the $n$-sphere ($n\geq 2$). They are applied to estimate solutions of quasilinear elliptic partial differential equations of $p$-Laplacian type, with combinations of Dirac measures on the right-hand side. The case $p=n$ is reduced to a problem on the sphere, using a conformal transformation. The cases when $1 < p < n $ and $p > $n are considered more briefly, full details being available in other papers of the author.