Work

On sharp singular Moser-Trudinger type inequalities and applications to zero mass (p,Q)-Laplace subelliptic equations in the Heisenberg group

Year: 2026

Type: article

Abstract: This article establishes a sharp singular Moser-Trudinger type inequality in a new function space and explores a concentration-compactness principle in the Heisenberg group, inspired by P.-L. Lions. We analyze the equivalence of sharp critical and subcritical singular Moser-Trudinger inequalities, focusing on their asymptotic behavior and connections between their suprema. Additionally, we apply the mountain pass theorem to demonstrate the existence of positive ground state solutions for zero mass ( 𝑝 , 𝑄 ) -Laplace subelliptic equations with singular exponential nonlinearity for the following equation: − Δ 𝐻 , 𝑝 ⁢ 𝑢 − Δ 𝐻 , 𝑄 ⁢ 𝑢 = 𝑓 ⁡ ( 𝜉 , 𝑢 ) 𝑟 ⁢ ( 𝜉 ) 𝜗 i n ℍ 𝑛 , with 1 < 𝑝 < 𝑄 , 𝜗 ∈ ( 0 , 𝑄 ) , 𝑄 = 2 ⁢ 𝑛 + 2 , the function 𝑟 ⁡ ( ⋅ ) is called the Korányi norm in ℍ 𝑛 and the nonlinearity 𝑓 : ℍ 𝑛 × ℝ → ℝ is a Carathéodory function, which behaves like e x p ⁡ ( 𝛼 ⁢ | 𝑠 | 𝑄 𝑄 − 1 ) as | 𝑠 | → + ∞ for some 𝛼 > 0 .

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114850

Authors: Giovany M. Figueiredo, Deepak Kumar Mahanta, Abhishek Sarkar

Institutions: Universidade de Brasília, Indian Institute of Technology Jodhpur

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550