Uniform Hölder continuity of approximate solutions to parabolic systems and its application
Nobuyuki Kato, Yoshihiko Yamaura · Communications in Partial Differential Equations · 2016
By means of a minimizing scheme, we constructively define approximate solutions to parabolic systems. On the basis of Campanato theory, these approximate solutions are shown to be locally Hölder equi-continuous with respect to an approximation parameter. As an application, we obtain a weak solution to an initial-boundary value problem with the same Hölder continuity.