Abstract
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ in Rn, n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there is an interval [An, 1/2n−An], where An→1, as n→∞, with μ-values for which the property does not hold. This interval is non-empty for n≥8.
Citation
Stefan Eilertsen. "On weighted positivity and the Wiener regularity of a boundary point for the fractional Laplacian." Ark. Mat. 38 (1) 53 - 75, March 2000. https://doi.org/10.1007/BF02384490
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