On the anisotropic critical $p$-Laplace equation: classification, decomposition, and stability results

Carlo Alberto Antonini; Giulio Ciraolo; Michele Gatti

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arXiv · 2604.13758

On the anisotropic critical $p$-Laplace equation: classification, decomposition, and stability results

Carlo Alberto Antonini·Giulio Ciraolo·Michele Gatti

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Abstract

We investigate both qualitative and quantitative issues related to the classification of non-negative energy solutions to the anisotropic critical $p$-Laplace equation in $\mathbb{R}^n$, for $1<p<n$. Specifically, we establish an anisotropic version of Struwe's decomposition, along with the interaction estimate for the family of bubbles in this decomposition. Moreover, we provide a short proof of the classification result as well as a quantitative stability result, proving that every energy solution to a perturbation of the anisotropic critical equation must be closed to a bubble, in the absence of bubbling.

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Carlo Alberto Antonini, Giulio Ciraolo, Michele Gatti. 2026-04-15. On the anisotropic critical $p$-Laplace equation: classification, decomposition, and stability results. https://arxiv.org/abs/2604.13758

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