A REMARK ON THE REGULARITY OF THE SOLUTIONS OF THE P-LAPLACIAN AND ITS APPLICATION TO THEIR FINITE-ELEMENT APPROXIMATION

In this paper, global H2 regularity is established for the solutions of the p-Laplacian equation, 1 < p ≤ 2, and related equations on domains which are either convex or have C2 boundaries, The results are used to derive some explicit error bounds for the finite element approximation of the p-Laplacian, which were not previously available because of the lack of regularity results. © 1993 Academic Press, Inc.