Symmetry results for critical anisotropic p-Laplacian equations in convex cones

• Published in: Geometric and functional analysis Vol. 30; no. 3; pp. 770 - 803
• Main Authors: Ciraolo, Giulio, Figalli, Alessio, Roncoroni, Alberto
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2020; Springer Nature B.V
• Subjects: Analysis; Cones; Critical point; Laplace equation; Mathematics; Mathematics and Statistics; Quasilinear anisotropic elliptic equations; Convex cones; 35B06; Sobolev embedding; 35J92; 35B33; Qualitative properties

Given n ≥ 2 and 1 < p < n , we consider the critical p -Laplacian equation Δ p u + u p ∗ - 1 = 0 , which corresponds to critical points of the Sobolev inequality. Exploiting the moving planes method, it has been recently shown that positive solutions in the whole space are classified. Since th...