TY - JOUR
AU - Pardo, R.
AU - Pereira, A.L.
AU - Sabina de Lis, J.C.
T1 - The tangential variation of a localized flux-type eigenvalue problem
LA - eng
PY - 2012
SP - 2104
EP - 2130
T2 - Journal of Differential Equations
SN - 0022-0396
VL - 252
IS - 3
AB - In this work the differentiability of the principal eigenvalue λ=λ1(Γ) to the localized Steklov problem -δu+qu=0 in Ω, ∂u∂ν=λχΓ(x)u on ∂Ω, where Γ⊂∂Ω is a smooth subdomain of ∂Ω and χΓ is its characteristic function relative to ∂Ω, is shown. As a key point, the flux subdomain Γ is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of λ1(Γ) with respect to Γ is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H1(Ω). The study is of interest in mathematical models in morphogenesis. © 2011 Elsevier Inc.
DO - 10.1016/J.JDE.2011.08.049
UR - https://portalciencia.ull.es/documentos/5de79a062999524dcbea4fda
DP - Dialnet - Portal de la Investigación
ER -