zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On two conjectures in the fixed membrane eigenvalue problem. (English) Zbl 0272.35058

35P99Spectral theory and eigenvalue problems for PD operators
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
Full Text: DOI
[1] R. Courant andD. Hilbert,Methods in Mathematical Physics, vol. 1. Interscience, New York (1953). · Zbl 0051.28802
[2] E. Hopf.A Remark on Linear Elliptic Differential Equations of Second Order. Proc. Amer. Math. Soc.3, 291--293 (1952). · Zbl 0048.07802 · doi:10.1090/S0002-9939-1952-0050126-X
[3] L. E. Payne,Isoperimetric Inequalities and their Applications, SIAM Review,9, 453--488 (1967). · Zbl 0154.12602 · doi:10.1137/1009070
[4] L. E. Payne andI. Stakgold,On the Mean Value of the Fundamental Mode in the Fixed Membrane Problem, J. Appl. Anal., to appear. · Zbl 0323.35057
[5] L. E. Payne andH. F. Weinberger,A Faber-Krahn Inequality for Wedge Like Domains, J. Math. Phys.39, 182--188 (1960). · Zbl 0099.18701
[6] G. Pólya andG. Szegö,Isoperimetric Inequalities in Mathematical Physics. Annals of Math. Studies #27, Princeton Univ. Press, Princeton (1951).