On W1,q Estimate for Weak Solutions to a Class of Divergence Elliptic Equations (Journal of Partial Differential Equations, 2002)
Local W^{1,q} estimates for weak solutions to a class of equations in divergence form D_i(a_{ij}(x)|Du|^{p-2D_ju) = 0 are obtained, where q > p is given. These estimates are very important in obtaining higher regularity for the weak solutions to elliptic equations.
Keywords: Divergence elliptic equation; local W^{1; q} estimate; reverse Hölder inequality