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

2025/02/17 by Michele Gatti, Gatti, Michele
#35B33 #35B35 #35J92 (Primary) 35B51 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.11759

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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