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arXiv · 2507.13027

Symmetrization on the sphere and applications

Satyanad Kichenassamy
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Abstract

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.

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Satyanad Kichenassamy. 2025-07-17. Symmetrization on the sphere and applications. https://arxiv.org/abs/2507.13027

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