A new formulation of Harnack's inequality for nonlocal operators

Comptes Rendus Mathematique

Volumn 349, Issue 11-12, 2011, Pages 637-640

  Kassmann, Moritz ^a  

^a BIELEFELD UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79959533361     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2011.04.014     Document Type: Article

References (10)

1. Bass R.F., Levin D.A. Harnack inequalities for jump processes. Potential Anal. 2002, 17(4):375-388.
2. Bass R.F., Levin D.A. Transition probabilities for symmetric jump processes. Trans. Amer. Math. Soc. 2002, 354(7):2933-2953. (electronic).
3. Bogdan K., Sztonyk P. Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian. Stud. Math. 2007, 181(2):101-123.
4. Chen Zh.-Qing, Kumagai T. Heat kernel estimates for stable-like processes on d-sets. Stochastic Process. Appl. 2003, 108(1):27-62.
5. Hansen W., Bliedtner J. Potential Theory: An Analytic and Probabilistic Approach to Balayage (Universitext) 1986, Springer, Berlin.
6. Axel Harnack C.-G. Die Grundlagen der Theorie des logarithmischen Potentiales und der eindeutigen Potentialfunktion in der Ebene 1887, Teubner, Leipzig, see also The Cornell Library Historical Mathematics Monographs online.
7. M. Kassmann, The classical Harnack inequality fails for nonlocal operators, Preprint No. 360, Sonderforschungsbereich 611, Universität Bonn, 2007.
8. Komatsu T. Uniform estimates for fundamental solutions associated with non-local Dirichlet forms. Osaka J. Math. 1995, 32(4):833-860.
9. Landkof N.S. Foundations of Modern Potential Theory 1972, Springer-Verlag, New York, translated from the Russian by A.P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften, Band 180.
10. Moser J. On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. 1961, 14:577-591.