PreprintCC BY-SA 4.0arXiv
A fractional critical problem in the halfspace with Neumann conditions
Abstract
Given s∈(0,1) and n>2s, we construct nontrivial solutions of the problem (−Δ)s u=u2*s−1 & in ℝn+, 𝒩s u=0& in ℝn-,where 𝒩s represents the nonlocal Neumann condition of exterior type.
Related
- A doubly nonlinear parabolic problem with variable exponents, homogeneous Neumann boundary conditions and generalized logistic source
- Sign-changing solutions for the critical Neumann problem in the three-dimensional unit ball
- Threshold phenomena for least energy solutions of a doubly critical Neumann problem with a critical absorption term
- Symmetry of solutions to nonlocal Neumann problems with the fractional Laplacian in half spaces
- Carleman estimates for a nonconservative Timoshenko beam involving Dirichlet-Neumann boundary conditions and application to exact controllability
BibTeX
@misc{delatorre2026fractional,
title = {{A fractional critical problem in the halfspace with Neumann conditions}},
author = {Azahara DelaTorre and Serena Dipierro and Angela Pistoia and Enrico Valdinoci},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.12890},
eprint = {2608.12890},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.12890},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - A fractional critical problem in the halfspace with Neumann conditions
AU - Azahara DelaTorre
AU - Serena Dipierro
AU - Angela Pistoia
AU - Enrico Valdinoci
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.12890
UR - https://arxiv.org/abs/2608.12890
AB - Given s∈(0,1) and n>2s, we construct nontrivial solutions of the problem (−Δ)^s u=u^2^*_s−1 & in ℝ^n_+, 𝒩_s u=0& in ℝ^n_-,where 𝒩_s represents the nonlocal Neumann condition of exterior type.
ER -