Mixed fully nonlinear local and nonlocal elliptic operators in Heisenberg group

Abstract

We establish the comparison principle, existence and regularity of solutions to the following problem concerning the mixed operator: (αM+λ,ΛD2HN ,Su- β- ∆HNs u = f in Ω,u = g in HN \ Ω, where M+λ,Λis the extremal Pucci's operator and (-∆HN)s denotes the fractional sub-Laplacian on Heisenberg group