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A self-contained proof of the variational characterization of the principal eigenvalue of −Δ+q under general Robin boundary conditions of non-classical type
Abstract
In this paper, we are going to deliver a completely self-contained proof of the variational characterization of the principal eigenvalue of −Δ+q in Ω under Robin boundary conditions of non-classical type, (∂ u)/(∂ n)+β(x)u=0 on ∂Ω, where β(x) is allowed to change sign on ∂Ω. The classical case occurs in the very special case when β≥ 0 on ∂Ω.
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BibTeX
@misc{lopezgomez2026selfcontained,
title = {{A self-contained proof of the variational characterization of the principal eigenvalue of $-Δ+q$ under general Robin boundary conditions of non-classical type}},
author = {Julián López-Gómez and Alejandro Sahuquillo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36457},
eprint = {2610.36457},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36457},
}
RIS
TY - UNPB
TI - A self-contained proof of the variational characterization of the principal eigenvalue of −Δ+q under general Robin boundary conditions of non-classical type
AU - Julián López-Gómez
AU - Alejandro Sahuquillo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36457
UR - https://arxiv.org/abs/2610.36457
AB - In this paper, we are going to deliver a completely self-contained proof of the variational characterization of the principal eigenvalue of −Δ+q in Ω under Robin boundary conditions of non-classical type, (∂ u)/(∂ n)+β(x)u=0 on ∂Ω, where β(x) is allowed to change sign on ∂Ω. The classical case occurs in the very special case when β≥ 0 on ∂Ω.
ER -