Commentarii Mathematici Helvetici

, Volume 69, Issue 1, pp 142–154

Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains

Authors

  • Giovanni Alessandrini
    • Dipartimento di Scienze MatematicheUniversità degli Studi di Trieste
Article

DOI: 10.1007/BF02564478

Cite this article as:
Alessandrini, G. Commentarii Mathematici Helvetici (1994) 69: 142. doi:10.1007/BF02564478
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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 nodal line of second eigenfunctions [P1], by removing theC smoothness assumption which is present in the original proof of Melas [M].

Copyright information

© Birkhäuser Verlag 1994