The Dirichlet problem for nonlocal elliptic equations
Rongrong Tian, Jinlong Wei, Yanbin Tang · Applicable Analysis · 2019
We study a class of nonlocal elliptic equations (−Δ)α/2ρ(x)−b(x)⋅∇ρ(x)=f(x) on a bounded domain Ω⊂Rd. For f∈Lq(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.