HIGHER-ORDER REGULARITY FOR THE SOLUTIONS OF SOME DEGENERATE QUASI-LINEAR ELLIPTIC-EQUATIONS IN THE PLANE

Local C(k,beta) and W2+k,v (k greater-than-or-equal-to 1,beta > 0, and v greater-than-or-equal-to 1) regularity is established for the solutions of a class of degenerate quasilinear elliptic equations, which include the p-Laplacian. Unlike the known local regularity results for such equations, k is larger than 2 in many notable cases. These results generalize those in [13], which were established only for the p-Laplacian. Furthermore, local results are extended to obtain a global regularity result in some cases. Global results of this type are essential in proving optimal error bounds for the finite element approximation of such equations.