SYMMETRY AND NONSYMMETRY FOR THE OVERDETERMINED STEKLOFF EIGENVALUE PROBLEM

Authors
ALESSANDRINI G MAGNANINI R
Citation
G. Alessandrini et R. Magnanini, SYMMETRY AND NONSYMMETRY FOR THE OVERDETERMINED STEKLOFF EIGENVALUE PROBLEM, Zeitschrift fur angewandte Mathematik und Physik, 45(1), 1994, pp. 44-52
Citations number
9
Categorie Soggetti
Mathematics,"Mathematical Method, Physical Science",Mathematics
Journal title
Zeitschrift fur angewandte Mathematik und Physik → ACNP
ISSN journal
00442275
Volume
45
Issue
1
Year of publication
1994
Pages
44 - 52
Database
ISI
SICI code
0044-2275(1994)45:1<44:SANFTO>2.0.ZU;2-5
Abstract
We consider the Stekloff eigenvalue problem (1.1)-(1.2); Payne and Phi lippin conjectured that if u is an eigenfunction which satisfies the o verdetermined condition \($) over bar Vu\ = 1 on partial derivative Om ega, then Omega should be a disk. In this paper we show that this conj ecture holds if and only if the complex potential F associated to u va nishes only at one point. Then we show how to construct non-symmetric domains in the case where F vanishes at more than one point.