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The Robin Function and Its Eigenvalues
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Bodo Dittmar
Published/Copyright:
March 10, 2010
Abstract
The paper deals with the Robin function and eigenvalue problems generated by the Robin operator. First we show that Green's function of an 𝑛-fold connected domain is the Robin function of an appropriate simply connected domain. The main part of the paper deals with eigenvalue problems for the Robin operator: the mixed Stekloff eigenvalue problem and the membrane problem with mixed boundary conditions. Isoperimetric inequalities are proved for the sum of reciprocal eigenvalues.
Received: 2007-03-12
Published Online: 2010-03-10
Published in Print: 2007-September
© Heldermann Verlag
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Articles in the same Issue
- The Robin Function and Its Eigenvalues
- Finite Dimensional Grading of the Virasoro Algebra
- On Nonmeasurable Subgroups of Uncountable Solvable Groups
- On a Priori Estimates of Solutions of Systems of Higher Order Nonlinear Functional-Differential Inequalities
- On Doubly Periodic Solutions of Nonlinear Hyperbolic Equations of Higher Order
- Analytic Function Theory in Algebras
- Complex Geometry of the Universal Teichmüller Space. II
- On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak
- Stagnation Zones of 𝐴-Solutions
- On a Periodic Boundary Value Problem for Fourth Order Linear Functional Differential Equations
- On the Stability in Bonnet's Theorem of the Surface Theory
- On Some Properties of Solutions of Polyharmonic Equation in Polyhedral Angles
- Generalized Analytic Functions in Higher Dimensions
