Partial regularity for degenerate parabolic systems with nonstandard growth and discontinuous coefficients

This article studies the partial Holder continuity of weak solutions to certain degenerate parabolic systems whose model is the parabolic p(x, t)-Laplacian system, partial derivative(t)u - div[mu(z)(1 + vertical bar Du vertical bar(2)) p(z)-2/2 Du] = 0, p(z) >= 2. Here, the exponential function p(z) satisfies a logarithmic continuity condition. We show that if mu(z) satisfies a certain VMO-type condition, then u is locally Holder continuous except for a measure zero set. (C) 2022 Elsevier Inc. All rights reserved.