On fully nonlinear PDEs derived from variational problems of L^p norms

The p-Laplace operator arises in the Euler-Lagrange equation associated with a minimizing problem which contains the L^pnorm of the gradient of functions. However, when we adapt a different L^pnorm equivalent to the standard one in the minimizing problem, a different p-Laplace-type operator appears in the corresponding Euler-Lagrange equation. First, we derive the limit PDE which the limit function of minimizers of those, as p → ∞, satisfies in the viscosity sense. Then we investigate the uniqueness and existence of viscosity solutions of the limit PDE.