Accessible Requires Authentication Published by De Gruyter June 27, 2010

Regularity in parabolic Dini continuous systems

Paolo Baroni
From the journal

Abstract

We consider a weak solution to the non-linear, parabolic systems of the form

ut – div A(x, t, u, Du) = 0,

where the vector field A satisfies a Dini-type continuity condition with respect to the variables (x, t, u), and we prove a partial regularity result for such a solution. Moreover, we give an estimate of the size of the singular set of a solution in terms of a generalized parabolic Hausdorff measure associated to an appropriate modulus of continuity naturally associated to the coefficients of the system.

Received: 2009-10-13
Revised: 2010-02-21
Published Online: 2010-06-27
Published in Print: 2011-November

© de Gruyter 2011