Numerical approximation of the first eigenpair of the p-Laplacian using finite elements and the penalty method

For 1 consider the eigenvalue problem for the p-Laplacian where . The first eigenvalue λ 1 can be obtained by minimizing the functional over . A method for computing λ 1 numerically is presented. The technique uses a finite element approximation to the first eigenfunction and a penalty function to enforce the constraint. Convergence is proved and numerical results are presented. The numerical results are compared with exact values when known. A lower bound for p -Laplacian eigenvalues is also presented. In particular, this work provides a computational framework for obtaining precise approximations of the best constant for the Sobolev imbedding .

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