The existence of weak solutions is studied to the initial Dirichlet problem of the equation , with inf . We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.
Changchun Liu. Junchao Gao. Songzhe Lian. "Existence of Solutions for the Evolution -Laplacian Equation Not in Divergence Form." J. Appl. Math. 2012 1 - 21, 2012. https://doi.org/10.1155/2012/835495