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On weighted positivity and the Wiener regularity of a boundary point for the fractional Laplacian
Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden.
2000 (English)In: Arkiv för matematik, ISSN 0004-2080, Vol. 38, no 1, 53-75 p.Article in journal (Refereed) Published
Abstract [en]

A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (-Delta)(mu) in R-n, ngreater than or equal to1, is obtained, for muis an element of(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 (-Delta)(mu), where the weight is a fundamental solution of this operator. It is shown that this property holds for mu as above while there is an interval [A(n), 1/2n - A(n)], where A(n) -->1, as n-->infinity, with mu-values for which the property does not hold. This interval is non-empty for ngreater than or equal to8.

Place, publisher, year, edition, pages
2000. Vol. 38, no 1, 53-75 p.
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-48949OAI: diva2:269845
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-14

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