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.
Abatangelo N., Jarohs S., Saldana A. (2018). On the loss of maximum principles for higher-order fractional laplacians. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 146(11), 4823-4835 [10.1090/proc/14165].
On the loss of maximum principles for higher-order fractional laplacians
Abatangelo N.;
2018
Abstract
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.File in questo prodotto:
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