Analysis of weak solutions' stability in the Dirichlet problem involving fractional operators on Heisenberg group, suggesting boundedness implications.
In this paper, we study the Dirichlet problem {Lsu(ξ)=f,ξ∈Ω,u(ξ)=g,ξ∈Hn∖Ω related to non-local integro-differential operator on the Heisenberg group Hn, where s∈(0,1), Ω⊂Hn is a bounded domain and Ls represents the fractional sub-Laplacian on Hn. By employing Vitali's convergence theorem and Prokhorov's theorem, we examine the stability of weak solutions to the integro-differential problem. Ultimately, the L∞ boundedness of weak solutions in relation to this Dirichlet problem is also established.
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Duan et al. (2025) studied this question.
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