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Some properties of Bessel functions with applications to Neumann eigenvalues in the unit disc

Ashu, Ashu Mathias LU (2013) In Bachelor's Theses in Mathematical Sciences MATK01 20122
Mathematics (Faculty of Sciences)
Abstract
A study is made of the multiplicities of the eigenvalues of the Laplace operator in the unit disc with Neumann boundary conditions. Our result is that all eigenvalues are simple or double, a result which is well-known if one instead considers Dirichlet boundary conditions. The result is proved by using some properties of Bessel functions. We also give an application to standing water waves in a cylinder.
Popular Abstract (Swedish)
Vi studerar multipliciteten av egenvärdena till Laplace-operatorn i enhetsskivan med Neumann-randvillkor. Vårt resultat är att alla egenvärden är enkla eller dubbla, ett resultat som är välkänt om man istället föreskriver Dirichlet-randvillkor. Beviset bygger på några egenskaper hos Besselfunktioner. Vi ger också en tillämpning på stående vattenvågor i en cylinder.
Please use this url to cite or link to this publication:
author
Ashu, Ashu Mathias LU
supervisor
organization
course
MATK01 20122
year
type
M2 - Bachelor Degree
subject
keywords
Bessel functions, Neumann eigenvalues, Bourget's hypothesis, unit disc, standing water waves
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFMA-4021-2013
ISSN
1654-6229
other publication id
2013:K1
language
English
id
7370411
date added to LUP
2015-06-18 11:15:15
date last changed
2015-12-21 15:18:41
@misc{7370411,
  abstract     = {A study is made of the multiplicities of the eigenvalues of the Laplace operator in the unit disc with Neumann boundary conditions. Our result is that all eigenvalues are simple or double, a result which is well-known if one instead considers Dirichlet boundary conditions. The result is proved by using some properties of Bessel functions. We also give an application to standing water waves in a cylinder.},
  author       = {Ashu, Ashu Mathias},
  issn         = {1654-6229},
  keyword      = {Bessel functions,Neumann eigenvalues,Bourget's hypothesis,unit disc,standing water waves},
  language     = {eng},
  note         = {Student Paper},
  series       = {Bachelor's Theses in Mathematical Sciences},
  title        = {Some properties of Bessel functions with applications to Neumann eigenvalues in the unit disc},
  year         = {2013},
}