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

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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References in corpus (1)

• A quantitative study of radial symmetry for solutions to semilinear equations in ${\mathbb{R}}^n$