Sobolev inequalities for fractional Neumann Laplacians on half spaces

Abstract

We consider different fractional Neumann Laplacians of order s ∈ (0, 1) on domains ω ⊂ ℝn, namely, the restricted Neumann Laplacian (-ΔωN)Rs, the semirestricted Neumann Laplacian (-ΔωN)Srs and the spectral Neumann Laplacian (-ΔωN)Sps. In particular, we are interested in the attainability of Sobolev constants for these operators when ω is a half-space.