TY - JOUR

T1 - Sobolev inequalities for fractional Neumann Laplacians on half spaces

AU - Musina, Roberta

AU - Назаров, Александр Ильич

PY - 2018/10/11

Y1 - 2018/10/11

N2 - We consider different fractional Neumann Laplacians of order s ∈ (0, 1) {s\in(0,1)} on domains Ω ω n {\Omega\subset\mathbb{R}^{n}}, namely, the restricted Neumann Laplacian (- Δ Ω N) R s {{(-\Delta-{\Omega}^{N})^{s}-{\mathrm{R}}}}, the semirestricted Neumann Laplacian (- Δ Ω N) Sr s {{(-\Delta-{\Omega}^{N})^{s}-{\mathrm{Sr}}}} and the spectral Neumann Laplacian (- Δ Ω N) Sp s {{(-\Delta-{\Omega}^{N})^{s}-{\mathrm{Sp}}}}. In particular, we are interested in the attainability of Sobolev constants for these operators when Ω is a half-space.

AB - We consider different fractional Neumann Laplacians of order s ∈ (0, 1) {s\in(0,1)} on domains Ω ω n {\Omega\subset\mathbb{R}^{n}}, namely, the restricted Neumann Laplacian (- Δ Ω N) R s {{(-\Delta-{\Omega}^{N})^{s}-{\mathrm{R}}}}, the semirestricted Neumann Laplacian (- Δ Ω N) Sr s {{(-\Delta-{\Omega}^{N})^{s}-{\mathrm{Sr}}}} and the spectral Neumann Laplacian (- Δ Ω N) Sp s {{(-\Delta-{\Omega}^{N})^{s}-{\mathrm{Sp}}}}. In particular, we are interested in the attainability of Sobolev constants for these operators when Ω is a half-space.

KW - Fractional Laplace operators

KW - Sobolev inequality

KW - lack of compactness

UR - http://www.scopus.com/inward/record.url?scp=85054988107&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/sobolev-inequalities-fractional-neumann-laplacians-half-spaces

U2 - 10.1515/acv-2018-0020

DO - 10.1515/acv-2018-0020

M3 - Article

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

SN - 1864-8258

ER -