PreprintarXiv licencearXiv
Variational characterization of principal eigenvalues for a general class of linear weighted BVP's under mixed boundary conditions of non-classical type
Abstract
The main goal of this paper is to characterize the existence of principal eigenvalues of { ll −div(A∇ u) +qu=λm u & in Ω, [1ex] ℬ u = 0 & on ∂ Ω, . where m∈ L∞(Ω) satisfies some of the conditions (A1)-(A3) below, as well as to deliver their variational characterizations whenever they exist. As we are dealing with general boundary operators of mixed non-classical type, in the general setting of this paper our results are far more general than all existing results. The case when m satisfies (A2) has not been previously explored in the literature.
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BibTeX
@misc{lopezgomez2026variational,
title = {{Variational characterization of principal eigenvalues for a general class of linear weighted BVP's under mixed boundary conditions of non-classical type}},
author = {Julián López-Gómez and Alejandro Sahuquillo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39940},
eprint = {2610.39940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39940},
}
RIS
TY - UNPB
TI - Variational characterization of principal eigenvalues for a general class of linear weighted BVP's under mixed boundary conditions of non-classical type
AU - Julián López-Gómez
AU - Alejandro Sahuquillo
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39940
UR - https://arxiv.org/abs/2610.39940
AB - The main goal of this paper is to characterize the existence of principal eigenvalues of { ll −div(A∇ u) +qu=λm u & in Ω, [1ex] ℬ u = 0 & on ∂ Ω, . where m∈ L^∞(Ω) satisfies some of the conditions (A1)-(A3) below, as well as to deliver their variational characterizations whenever they exist. As we are dealing with general boundary operators of mixed non-classical type, in the general setting of this paper our results are far more general than all existing results. The case when m satisfies (A2) has not been previously explored in the literature.
ER -