A high regularity result of solutions to modified p-Stokes equations

摘要

This paper is concerned with a special quasilinear elliptic system, which can be seen as a perturbed p-Laplacean, p is an element of (1, 2), in the whole space R-n. For its "shape'', it is close to the p-Stokes system. However, our quasilinear second-order differential operator is given by means of del u and not by its symmetric part, so that our system cannot be considered as a p-Stokes system. Hence, it is called modified p-Stokes system. We look for the high regularity of the solutions (u, pi), in the sense of D(2)u, del pi is an element of L-q(R-n), q is an element of (n, infinity). In particular, we get del u, pi is an element of C-0,C-alpha (R-n). As far as we know, such a result of high regularity is the first concerning the coupling of unknowns (u, pi). However, our result also holds for the p-Laplacean, and it is the first high regularity result in an unbounded domain. (C) 2014 Elsevier Ltd. All rights reserved.