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On the loss of maximum principles for higher-order fractional laplacians

par Abatangelo, Nicola ;Jarohs, Sven;Saldaña, Alberto
Référence Proceedings of the American Mathematical Society, 146, 11, page (4823-4835)
Publication Publié, 2018

Article révisé par les pairs

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Résumé :

We study the existence and positivity of solutions to problems involving higher-order fractional Laplacians (−Δ)s for any s > 1. In particular, using a suitable variational framework and the nonlocal properties of these operators, we provide an explicit counterexample to general maximum principles for s ∈ (n, n + 1) with n ∈ ℕ odd, and we mention some particular domains where positivity preserving properties do hold.