New isoperimetric inequalities in mathematical physics. (English) Zbl 0814.35083

Alvino, Angelo (ed.) et al., Partial differential equations of elliptic type. Proceedings of the conference held October 12-16, 1992 in Cortona, Italy. Cambridge: University Press. Symp. Math. 35, 197-203 (1994).
The main result is the isoperimetric inequality for clamped plates. Lord Rayleigh conjectured that among all clamped plates of given area the circle has the lowest principal frequency. Partial proofs were given by Szegö and Talenti. The author was able to fill the gaps and to establish Rayleigh’s conjecture.
The second part deals with isoperimetric inequalities between the capacity and the moment of inertia. The author extends a result of Pólya and Szegö for simply connected domains in the plane to arbitrary Borel sets.
For the entire collection see [Zbl 0799.00025].
Reviewer: C.Bandle (Basel)


35P15 Estimates of eigenvalues in context of PDEs
74K20 Plates