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arXiv · 2502.11759

Approximate radial symmetry for $p$-Laplace equations via the moving planes method

Michele Gatti
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Abstract

We investigate quasi-symmetry for small perturbations of the Gidas-Ni-Nirenberg problem involving the $p$-Laplacian and for small perturbations the critical $p$-Laplace equation for $p>2$. To achieve these results, we provide a quantitative review of the work by Damascelli & Sciunzi (Calc. Var. Partial Differential Equations 25 (2006), no. 2, 139-159) concerning the weak Harnack comparison inequality and the local boundedness comparison inequality. Moreover, we prove a comparison principle for small domains.

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Michele Gatti. 2025-02-17. Approximate radial symmetry for $p$-Laplace equations via the moving planes method. https://doi.org/10.1007/s00526-025-03129-9

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