an:00590902
Zbl 0838.35006
Alessandrini, Giovanni
Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains
EN
Comment. Math. Helv. 69, No. 1, 142-154 (1994).
00019072
1994
j
35B05 35P05 35J05 58J50 35J67
boundary behavior of nodal lines; second eigenfunctions
Summary: We describe the boundary behavior of the nodal lines of eigenfunctions of the fixed membrane problem in convex, possibly nonsmooth, domains. This result is applied to the proof of Payne's conjecture on the nodal line of second eigenfunctions, by removing the \(C^\infty\) smoothness assumption which is present in the original proof of \textit{A. D. Melas} [J. Differ. Geom. 35, No. 1, 255-263 (1992; Zbl 0769.58056)].
Zbl 0769.58056