Regularity for minimizers with positive Jacobian

摘要

We deal with maps u : . Rn. Rn minimizing variational integrals [|Du(x)|p + h(det Du(x))] dx, where 2 = p < n, h : (0,+8). [0,+8) is convex and blows when det Du. 0+: limt.0+ h(t) = +8. If such a blow up is a power of | ln(t)|, then we derive regularity for the minimizer u = (u1,..., un). We are able also to dealwith integrals containing all theminors: [|Du(x)|p + n-1 s=2 |adjs(Du(x))|qs + h(det Du(x))] dx with q(s) >= 1.