Partial regularity results for evolutional p-Laplacian systems with natural growth

 We study a regularity for evolutional p-Laplacian systems with natural growth on the gradient. It is shown that weak solutions of small image and their gradients are partial H?lder continuous and the size of the exceptional set for regularity is estimated in terms of Hausdorff measure. The main ingredient is to improve the Gehring inequality, which implies the higher integrability of the gradient and was first developed by Kinnunen and Lewis, so as to be well-worked in our perturbation estimate. We also use a refinement of the perturbation argument and make a device for H?lder estimates of the gradient. Received: 4 March 2002 Mathematics Subject Classification (2000): Primary 35D10, 35B65, 35K65