Asymptotic behavior of the p-torsion functions as p goes to 1

摘要

Let be a Lipschitz bounded domain of , , and let denote the p-torsion function of , p > 1. It is observed that the value 1 for the Cheeger constant is threshold with respect to the asymptotic behavior of u (p) , as , in the following sense: when , one has , and when , one has . In the case , it is proved that . For a radial annulus , with inner radius a and outer radius b, it is proved that when h(Omega(a,b)) = 1.