Eigenvalues and Eigenfunctions of −∆ for an R Unit Ball and Related Theorems

@inproceedings{Serrano2018EigenvaluesAE,
  title={Eigenvalues and Eigenfunctions of −∆ for an R Unit Ball and Related Theorems},
  author={H. Gim{\'e}nez Serrano and Francisco Jos{\'e} de C{\'a}ldas},
  year={2018}
}
The present work computes the eigenvalues and eigenfunctions of the Laplacian operator, −∆, for a particular situation where Ω = B1(0) ⊂ R2. To this end, separation of variables was used together with the bounded solutions of Bessel’s differential equations. This problem set may arise, for example, when solving a wave equation representing the vibration associated to an elastic circular membrane for N = 2 and Ω = B1(0). A set of theorems related to the present analysis are shown at the end of… CONTINUE READING

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