PreprintarXiv licencearXiv
Boundary regularity of k-Hessian eigenfunctions
Abstract
We prove smoothness up to the boundary for k-Hessian eigenfunctions on smooth bounded uniformly convex domains when 2≤ k<n. This resolves an open problem in the regularity theory of degenerate fully nonlinear elliptic equations and extends the boundary smoothness theorem for Monge--Ampère eigenfunctions. In contrast to the Monge--Ampère case, the linearized k-Hessian operator remains uniformly elliptic up to the boundary.
Related
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- Near-boundary rigidity and strict maximum modulus for Neumann eigenfunctions on convex planar domains
BibTeX
@misc{qiu2026boundary,
title = {{Boundary regularity of $k$-Hessian eigenfunctions}},
author = {Guohuan Qiu and Jin Yan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31445},
eprint = {2610.31445},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31445},
}
RIS
TY - UNPB
TI - Boundary regularity of k-Hessian eigenfunctions
AU - Guohuan Qiu
AU - Jin Yan
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31445
UR - https://arxiv.org/abs/2610.31445
AB - We prove smoothness up to the boundary for k-Hessian eigenfunctions on smooth bounded uniformly convex domains when 2≤ k<n. This resolves an open problem in the regularity theory of degenerate fully nonlinear elliptic equations and extends the boundary smoothness theorem for Monge--Ampère eigenfunctions. In contrast to the Monge--Ampère case, the linearized k-Hessian operator remains uniformly elliptic up to the boundary.
ER -