Asymptotically regular problems I: Higher integrability (Q846969)

The paper deals with the regularity of the weak solutions \(u\) of nonlinear systems of partial differential equations. By assuming that the system has a suitable condition of asymptotic elliptic behavior near infinity, the authors prove a result of higher integrability for the gradient \(Du\). The Hölder continuity of \(u\) is obtained in low dimensions. The results hold also for minimizers of variational integrals. Moreover, some properties for generalized minimizers are also considered, by applying the results in the context of the relaxation theory.