TY - JOUR
T1 - On Stekloff eigenvalue problem
AU - Chen, Roger
AU - Sung, Chiung Jue
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2000/10
Y1 - 2000/10
N2 - Let (Mn, g) be a smooth compact Riemannian manifold with boundary ∂M ≠ 0. In this article we discuss the first positive eigenvalue of the Stekloff eigenvalue problem {(-Δ + q)u(x) = 0 in M ∂u/∂v = λu on ∂M, where q(x) is a C2 function defined on M, ∂vg is the normal derivative with respect to the unit outward normal vector on the boundary ∂M. In particular, when the boundary ∂M satisfies the "interior rolling R-ball" condition, we obtain a positive lower bound for the first nonzero eigenvalue in terms of n, the diameter of M, R, the lower bound of the Ricci curvature, the lower bound of the second fundamental form elements, and the tangential derivatives of the second fundamental form elements.
AB - Let (Mn, g) be a smooth compact Riemannian manifold with boundary ∂M ≠ 0. In this article we discuss the first positive eigenvalue of the Stekloff eigenvalue problem {(-Δ + q)u(x) = 0 in M ∂u/∂v = λu on ∂M, where q(x) is a C2 function defined on M, ∂vg is the normal derivative with respect to the unit outward normal vector on the boundary ∂M. In particular, when the boundary ∂M satisfies the "interior rolling R-ball" condition, we obtain a positive lower bound for the first nonzero eigenvalue in terms of n, the diameter of M, R, the lower bound of the Ricci curvature, the lower bound of the second fundamental form elements, and the tangential derivatives of the second fundamental form elements.
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U2 - 10.2140/pjm.2000.195.277
DO - 10.2140/pjm.2000.195.277
M3 - Article
AN - SCOPUS:0040778226
SN - 0030-8730
VL - 195
SP - 277
EP - 296
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 2
ER -