zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
An eigenvalue problem with mixed boundary conditions and trace theorems. (English) Zbl 1141.35040
Summary: An eigenvalue problem is considered where the eigenvalue appears in the domain and on the boundary. This eigenvalue problem has a spectrum of discrete positive and negative eigenvalues. The smallest positive and the largest negative eigenvalue λ ±1 can be characterized by a variational principle. We are mainly interested in obtaining non-trivial upper bounds for λ -1 . We prove some domain monotonicity for certain special shapes using a kind of maximum principle derived by C. Bandle, J. von Bellow and W. Reichel in [J. Eur. Math. Soc. (JEMS) 10, No. 1, 73–104 (2008; Zbl 1167.35012)]. We then apply these bounds to the trace inequality.
MSC:
35P15Estimation of eigenvalues and upper and lower bounds for PD operators
49R50Variational methods for eigenvalues of operators (MSC2000)
51M16Inequalities and extremum problems (geometry)