The Dirichlet problem for nonlocal elliptic equations. Issue 10 (27th July 2021)

• Record Type: Journal Article
• Authors: Tian, Rongrong; Wei, Jinlong; Tang, Yanbin
• Is Part Of: Applicable analysis. Volume 100:Issue 10(2021)
• Page Start: 2093
• Page End: 2107
• Publication Date: 2021-07-27
• Subjects: Y. Ou; Vanishing viscosity solution -- existence -- uniqueness -- measure-valued nonlocal equation; 35R06 -- 35S15 -- 60H15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1677893
• Languages: English
• ISSNs: 0003-6811

Abstract

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.