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Asymptotics for the principal eigenvalue of the \(p\)-Laplacian on the ball as \(p\) approaches 1. (English) Zbl 1281.35064

Summary: Using the estimates of the principal eigenvalue of the \(p\)-Laplacian on the ball from below and from above, we provide its asymptotic analysis as \(p\to 1_+\).

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
49R05 Variational methods for eigenvalues of operators
33B15 Gamma, beta and polygamma functions
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