Regularity for quasi-linear degenerate elliptic equations with VMO coefficients

In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A(x, u) satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B(x, u, .u) satisfies the subcritical growth (1.2). In particular, when F(x) . L q(.) and f(x) . L .(.) with q, . > max {p, n} for any 1 < p < + ., we obtain interior Hölder continuity of any weak solution of (1.1) u . C 0,.loc (.) with an index . = min {1 . n/q, 1 . n/.}.