Limit of p-Laplacian obstacle problems
In this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as p → ∞ {p oinfty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in ω or for data f (that do not change sign in ω) possibly vanishing in a set of positive measure.