NODAL LINES OF EIGENFUNCTIONS OF THE FIXED MEMBRANE PROBLEM IN GENERAL CONVEX DOMAINS

Authors
ALESSANDRINI G
Citation
G. Alessandrini, NODAL LINES OF EIGENFUNCTIONS OF THE FIXED MEMBRANE PROBLEM IN GENERAL CONVEX DOMAINS, Commentarii mathematici helvetici, 69(1), 1994, pp. 142-154
Citations number
15
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Commentarii mathematici helvetici → ACNP
ISSN journal
00102571
Volume
69
Issue
1
Year of publication
1994
Pages
142 - 154
Database
ISI
SICI code
0010-2571(1994)69:1<142:NLOEOT>2.0.ZU;2-9
Abstract
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 noda l line of second eigenfunctions [P1], by removing the Cinfinity smooth ness assumption which is present in the original proof of Melas [M].