Generalized Picone and Riccati inequalities for half-linear differential operators with arbitrary elliptic matrices.
Gradient estimates for the p(x)-Laplacian equation in
Under some assumptions on the function p(x), we obtain global gradient estimates for weak solutions of the p(x)-Laplacian type equation in .
Gradient estimation of a -harmonic map.
Gradient regularity via rearrangements for -Laplacian type elliptic boundary value problems
A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.