Potential Analysis

, Volume 45, Issue 1, pp 187–200 | Cite as

Liouville Theorems for a General Class of Nonlocal Operators

  • Mouhamed Moustapha Fall
  • Tobias WethEmail author


In this paper, we study the equation \(\mathcal {L} u=0\) in \(\mathbb {R}^{N}\), where \(\mathcal {L}\) belongs to a general class of nonlocal linear operators which may be anisotropic and nonsymmetric. We classify distributional solutions of this equation, thereby extending and generalizing recent Liouville type theorems in the case where \(\mathcal {L}= (-{\Delta })^{s}\), s ∈ (0, 1) is the classical fractional Laplacian.


Nonlocal elliptic equations Liouville theorem Anisotropic operator 

Mathematics Subject Classification (2010)

35R11 35B40 35J75 47B25 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.African Institute for Mathematical Sciences (A.I.M.S.) of SenegalMbourSénégal
  2. 2.Goethe-Universität Frankfurt, Institut für MathematikFrankfurtGermany

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