Inserted: 2 nov 2004
Last Updated: 30 oct 2005
Journal: Ann. Inst. H. Poincare Anal. Non Lineaire
We present a new approach to the partial regularity of solutions to non-linear, second order parabolic systems of the form $$ut - div a(x,t,u,Du) =0.$$ We introduce the A-caloric approximation lemma, a parabolic analogue of the harmonic approximation lemma of De Giorgi. This allows to prove optimal partial regularity results for solutions in an elementary way, under natural assumptions and without requiring a priori regularity of solutions such as boundedness or Hölder continuity, as commonly done. After partial regulariy, we provide bounds for the parabolic Hausdorff dimension of singular sets of solutions.