Semilinear fractional elliptic equations involving measures
نویسندگان
چکیده
We study the existence of weak solutions to (E) (−∆)u+g(u) = ν in a bounded regular domain Ω in R (N ≥ 2) which vanish in R \Ω, where (−∆) denotes the fractional Laplacian with α ∈ (0, 1), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses. When g satisfies a subcritical integrability condition, we prove the existence and uniqueness of a weak solution for problem (E) for any measure. In the case where ν is Dirac measure, we characterize the asymptotic behavior of the solution. When g(r) = |r|r with k supercritical, we show that a condition of absolute continuity of the measure with respect to some Bessel capacity is a necessary and sufficient condition in order (E) to be solved.
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