Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

Ben Andrews, Julie Clutterbuck

Published 2013-06-06Version 1

We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.