PARTIAL REGULARITY OF MINIMIZERS OF HIGHER ORDER INTEGRALS WITH (p, q)-GROWTH

We consider higher order functionals of the form F[u] = integral(Omega) f(D-m u)dx for u : R-n superset of Omega -> R-N, where the integrand f : circle dot(m) (R-n, R-N) -> R, m >= 1 is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the (p, q)-growth condition gamma vertical bar A vertical bar(p) <= f(A) <= L(1+vertical bar A vertical bar(q)) for all A is an element of circle dot(m) (R-n, R-N), with gamma, L > 0 and 1 < p <= q < min {p + 1/n, 2n-1/2n-1p}. We study minimizers of the functional Finverted right perpendicular.inverted left perpendicular and prove a partial C-loc(m,alpha)-regularity result.