The Dirichlet problem for nonlocal elliptic equations. Issue 10 (27th July 2021) - Tian, Rongrong; Wei, Jinlong; Tang, Yanbin
Abstract : We study a class of nonlocal elliptic equations ( − Δ ) α / 2 ρ ( x ) − b ( x ) ⋅ ∇ ρ ( x ) = f ( x ) on a bounded domain Ω ⊂ R d . For f ∈ L q ( Ω ) ( q > d / α ), by the Lax–Milgram theorem and the De Giorgi iteration, we prove the existence and uniqueness of L ∞ solution. Furthermore, we investigate the existence of densities for measure-valued solutions to nonhomogeneous measure-valued nonlocal elliptic equations.