The asymptotic behaviour of the solutions to widely degenerate p-Laplace equations

In this paper, we consider the Dirichlet problems with a widely degenerate equation. Through a well-known result by Talenti, we explicitly express the gradient of the solution uₚ outside the ball with a radius of $1$, if the datum f is a non-negative radially decreasing function. This allows us to analyze the behaviour of uₚ as p → 1⁺ and to establish some higher regularity results, assuming the datum f in a suitable Lorentz space.