Classification of positive solutions of critical anisotropic Sobolev equation without the finite volume constraint

In this paper, we classify all positive solutions of the critical anisotropic Sobolev equation {equation*} -ΔHₚu = u^{p*-1}, \ \ x∈ R^n {equation*} without the finite volume constraint for n ≥ 2 and (n+1)/3 ≤ p < n, where p* = np/n-p denotes the critical Sobolev exponent and -ΔHₚ=-div(Hᵖ⁻¹(·)∇ H(·)) denotes the anisotropic p-Laplace operator. This result removes the finite volume assumption on the classification of critical anisotropic p-Laplace equation which was obtained by Ciraolo-Figalli-Roncoroni in the literature {CFR}. The method is based on constructing suitable vector fields integral inequality and using Newton's type inequality.