The first non-zero Neumann p-fractional eigenvalue

Abstract

Abstract. In this work we study the asymptotic behavior of the first nonzero Neumann p−fractional eigenvalue λ 1 (s, p) as s → 1 − and as p → ∞. We show that there exists a constant K such that K(1 − s)λ 1 (s, p) goes to the first non-zero Neumann eigenvalue of the p−Laplacian. While in the limit case p → ∞, we prove that λ 1 (1, s) 1/p goes to an eigenvalue of the Hölder ∞−Laplacian.