On a Generalized Prandtl–Batchelor Free Boundary Problem With a Singularity on a Stratified Lie Group
Year: 2026
Type: article
Abstract: We investigate a class of elliptic free boundary problems, including a generalized Prandtl–Batchelor type problem with a singularity on a stratified Lie group. The associated energy functional is nondifferentiable, which precludes the direct application of standard variational techniques. To address this challenge, we approximate the energy functional using a sequence of C 1 -functionals and establish the existence of at least two distinct nontrivial solutions. Our analysis combines elliptic regularity theory with the mountain pass theorem in a non-Euclidean setting.
Source: Asymptotic Analysis
Author: Sabri Bensid
Institution: University of Abou Bekr Belkaïd
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406230947