A duality approach to the fractional Laplacian with measure data

Kenneth H. Karlsen, Francesco Petitta, Süleyman Ulusoy

Type: Article

Publication Date: 2011-01-01

Citations: 48

DOI: https://doi.org/10.5565/publmat_55111_07

Abstract

We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems likewith vanishing conditions at infinity.Here µ is a bounded Radon measure whose support is compactly contained in R N , N ≥ 2, and -(∆) s is the fractional Laplace operator of order s ∈ (1/2, 1).

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