Harnack Inequalities for Non-local Operators of Variable Order
نویسندگان
چکیده
We consider harmonic functions with respect to the operator Lu(x) = ∫ [u(x+ h)− u(x)− 1(|h|≤1)h · ∇u(x)]n(x, h) dh. Under suitable conditions on n(x, h) we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator L is allowed to be anisotropic and of variable order.
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