Mixed fully nonlinear local and nonlocal elliptic operators in Heisenberg group

2023/01/09 by Priyank Oza, Oza, Priyank, Jagmohan Tyagi +1 · 1 citation
Computer Science · Mathematics · #35A01 #35D40 #35J60 #35R03 #47G20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2301.03253

openalex publication_date 2023/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the comparison principle, existence and regularity of viscosity solutions to the following problem concerning the mixed operator: \begincases αM⁺_λ,Λ(D²_\mathbbmH^N,Su)-β(-Δ_\mathbbmH^N)^su=f amp;in Ω, u=g amp;in \mathbbmH^N∖Ω, \endcases where M_λ,Λ⁺ is the extremal Pucci's operator and (-Δ_\mathbbmH^N)^s denotes the fractional sub-Laplacian on Heisenberg group. Here α≥ 0 and β>0 are constants.

Citations

• Fine boundary regularity for fully nonlinear mixed local-nonlocal problems
• Regularity of solutions to variable-exponent degenerate mixed fully nonlinear local and nonlocal equations

Cited by

• Fujita exponent for the fractional sub-Laplace semilinear heat equation with forcing term on the Heisenberg group

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