The paper establishes an anisotropic Struwe decomposition with bubble interaction estimates, a short classification proof, and quantitative stability for perturbations of the anisotropic critical p-Laplace equation.
Sharp stability for critical points of the Sobolev inequality in the absence of bubbling
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
When $u$ is close to a single Talenti bubble $v$ of the $p$-Sobolev inequality, we show that \begin{equation*} \|Du-Dv\|_{L^p(\mathbb{R}^n)}^{\max\{1,p-1\}}\le C \|-{\rm div}(|Du|^{p-2}Du)-|u|^{p^*-2}u\|_{W^{-1,q}(\mathbb{R}^n)}, \end{equation*} where $C=C(n,p)>0$. This estimate provides a sharp stability estimate for the Struwe-type decomposition in the single bubble case, generalizing the result of Ciraolo, Figalli, and Maggi \cite{CFM2018} (focusing on the case $p=2$) to the arbitrary $p$. Also, in the Sobolev setting, this answers an open problem raised by Zhou and Zou in \cite[Remark 1.17]{ZZ2023}.
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math.AP 2years
2026 2representative citing papers
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On the anisotropic critical $p$-Laplace equation: classification, decomposition, and stability results
The paper establishes an anisotropic Struwe decomposition with bubble interaction estimates, a short classification proof, and quantitative stability for perturbations of the anisotropic critical p-Laplace equation.
- Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$