Some new ideas for a Schiffer’s conjecture. (English) Zbl 0881.35083
Malanowski, Kazimierz (ed.) et al., Modelling and optimization of distributed parameter systems. Applications to engineering. Papers from the IFIP WG 7.2 conference held in Warsaw (Poland), July 17–21, 1995. London: Chapman & Hall. 90-97 (1996).
Summary: We discuss a Schiffer’s conjecture which is a symmetry problem for an overdetermined spectral PDE. We show the connection between this problem and the critical points of the eigenvalue with a volume constraint as well as the Faber-Krahn inequality. We give two original proofs of these symmetry results in the case of the first eigenvalue.
For the entire collection see [Zbl 0865.00062].
For the entire collection see [Zbl 0865.00062].
MSC:
| 35P05 | General topics in linear spectral theory for PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
