Lower semicontinuity of weak supersolutions to nonlinear parabolic equations

Abstract

We prove that weak supersolutions to equations similar to the evolutionary $p$-Laplace equation have lower semicontinuous representatives. The proof avoids the use of Harnack's inequality and, in particular, the use of parabolic BMO. Moreover, the result gives a new point of view to approaching the continuity of the solutions to a second-order partial differential equation in divergence form.