A Modification of the Blowup Technique for Variational Integrals with Subquadratic Growth

We present a version of the blowup technique which applies to local minimizers u: VªRN, V open in Rn, of strictly convex variational integrals J u.[ H f =u. dx, where f is of p-growth for some 1-p-2. This provides an alterna- V tive approach towards the partial regularity theorem of Anzellotti and Giaquinta. For two-dimensional problems we obtain everywhere C1, a-regularity