Geodesic
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian
Krzysztof Bogdan 1   ; Paweł Sztonyk 2
1 Institute of Mathematics Polish Academy of Sciences and Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
2 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Studia Mathematica, Tome 181 (2007) no. 2, pp. 101-123 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.
DOI : 10.4064/sm181-2-1
Keywords: characterize those homogeneous translation invariant symmetric non local operators positive maximum principle whose harmonic functions satisfy harnacks inequality estimate corresponding semigroup potential kernel

Krzysztof Bogdan  1   ; Paweł Sztonyk  2

1 Institute of Mathematics Polish Academy of Sciences and Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
2 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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     title = {Estimates of the potential kernel and {Harnack's} inequality for the anisotropic fractional {Laplacian}},
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Krzysztof Bogdan; Paweł Sztonyk. Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian. Studia Mathematica, Tome 181 (2007) no. 2, pp. 101-123. doi: 10.4064/sm181-2-1

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