Mixed local-nonlocal p-Laplace equation with variable singular nonlinearity in the Heisenberg group

2025/12/12 by Garain, Prashanta
Mathematics · #35A02 #35J62 #35J75 #35R03 #35R11 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2512.11442

openalex publication_date 2025/12/12 · openalex created_date 2025/12/16 · openalex updated_date 2026/07/28

Abstract

We investigate a mixed local-nonlocal p-Laplace equation on the Heisenberg group, where the nonlinear term features a variable singular exponent. Our analysis establishes the existence, uniqueness, and regularity of weak solutions under suitable structural assumptions. To the best of our knowledge, this work provides the first treatment of such mixed local-nonlocal problems in a non-commutative setting, even in the linear case p=2 with a constant singular exponent.

Citations

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Related

• Nonlocal singular problem and associated Sobolev type inequality with extremal in the Heisenberg group
• On mixed local-nonlocal Sobolev-type inequalities and their connection with singular equations in the Heisenberg group
• On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems
• Regularity theory for nonlocal equations with general growth in the Heisenberg group
• The Fujita exponent for a heat equation with mixed local and nonlocal nonlinearities on the Heisenberg group