Abstract:

This talk will present a differential identity for a class of p-Laplace equations and classify all positive finite-energy cylindrically symmetric solutions of Equation (1.2) for 3 ≤ k ≤ n−1. The work addresses the Euler-Lagrange equation associated with Hardy-Mazya-Sobolev inequalities:

-Δₚu = u^(p*(1)−1) / |y| in ℝⁿ,
u > 0,
u ∈ D^(1,p)(ℝⁿ),

where p*(1) = p(n−1)/(n−p), x = (y,z), and ℝⁿ = ℝᵏ × ℝⁿ⁻ᵏ. The results yield the best constant and extremal function for these inequalities, resolving a conjecture posed by Alvino-Ferone-Trombetti (2006) for 1 < p < n. This is joint work with Daowen Lin.

Background:

For p=2, this problem was solved by Mancini-Fabbri-Sandeep in 2006. Prof. Ma’s work extends these findings to the broader p-Laplace context.