ABSTRACT

In the present contribution we derive some a priori bounds for classical solutions of fully nonlinear parabolic equations that include possible time degeneracies. Moreover we show that, in general, a comparison principle for such equations cannot hold. The boundary conditions are of mixed type, a Dirichlet boundary condition on one part of the time lateral boundary and a possibly dynamical one on the complementary part. The latter includes as a special case the Neumann boundary condition.