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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References:

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