The ∞-eigenvalue problem

The Euler-Lagrange equation of the nonlinear Rayleigh quotient (integral(Omega) /del u\\(p) dx) /(integral(Omega) /u\(p) dx) is -div (/del u\(p-2)del u) = Lambda(p)(p/)u\(p-2)u, where Lambda(p)(p) is the minimum value of the quotient. The limit as p --> infinity of these equations is found to be max {Lambda(infinity) - /del u(x)\/u(x), Delta(infinity)u(x) } = 0, where the constant Lambda(infinity) = lim(p-->infinity) Lambda p is the reciprocal of the maximum of the distance to the boundary of the domain Omega.