Classification of positive ${\mathcal{D}}^{1,p}({\mathbb{R}}^N)$-solutions to the critical $p$-Laplace equation in ${\mathbb{R}}^N$

Abstract

We provide the classification of the positive solutions to $-{\Delta }_{p}u=u^{p^{\ast }-1}$ in ${\mathcal{D}}^{1,p}({\mathbb{R}}^N)$ in the case $2<p<N$. Since the case $1<p\le 2$ is already known this provides the complete classification for $1<p<N$.

Cited by in corpus (8)

• Sharp pointwise estimates for weighted critical $p$-Laplace equations
• Decay estimates and a vanishing phenomenon for the solutions of critical anisotropic equations
• Nondegeneracy of the bubble for the critical p-Laplace equation
• Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds
• Groundstate asymptotics for a class of singularly perturbed $p$-Laplacian problems in ${\mathbb{R}}^N$
• A quantitative study of radial symmetry for solutions to semilinear equations in ${\mathbb{R}}^n$
• Approximate radial symmetry for $p$-Laplace equations via the moving planes method
• Classification results for bounded positive solutions to the critical $p$-Laplace equation