TY - JOUR
AU - DE LIS, J.S.
AU - DE LEÓN, S.S.
T1 - The limit as p → 1 of the higher eigenvalues of the p-laplacian operator -δp
LA - eng
PY - 2021
SP - 1395
EP - 1439
T2 - Indiana University Mathematics Journal
SN - 0022-2518
VL - 70
IS - 4
PB - Department of Mathematics, Indiana University
AB - This work provides a direct proof of the existence for each n ∈ N of the limit λ(1),n := limp→1 λ(p),n of the n-th Ljusternik-Schnirelman Dirichlet eigenvalue λ(p),n of -Δp in a bounded Lipschitz domain Ω ⊂ RN. Most importantly, it is shown that λ(1),n defines an eigenvalue of the 1-Laplacian operator -Δ1, with a well-defined strong associated eigenfunction un ∈ BV(Ω). In the main results of the paper, the radial LS eigenvalues of -Δ1 are fully described, together with a detailed account on the profiles of their associated eigenfunctions. Our approach does not involve critical point theory for non-smooth functionals, although the definition of the LS-spectrum of -Δ1 relies on it.
DO - 10.1512/IUMJ.2021.70.8563
UR - https://portalciencia.ull.es/documentos/6145ab4f65b6b477913b42aa
DP - Dialnet - Portal de la Investigación
ER -