Local and global properties of solutions of quasilinear Hamilton-Jacobi equations

We study some properties of the solutions of (E) -Delta(p)u + vertical bar del u vertical bar(q) = 0 in a domain Omega subset of R-N, mostly when p >= q > p - 1. We give a universal a priori estimate of the gradient of the solutions with respect to the distance to the boundary. We give a full classification of the isolated singularities of the nonnegative solutions of (E), a partial classification of isolated singularities of the negative solutions. We prove a general removability result expressed in terms of some Bessel capacity of the removable set. We extend our estimates to equations on complete noncompact manifolds satisfying a lower bound estimate on the Ricci curvature, and derive some Liouville type theorems. (C) 2014 Elsevier Inc. All rights reserved.