  We study a parabolic Ventsell problem for a second order differential
operator in divergence form and with interior and boundary drift terms on the
snowflake domain. We prove that under standard conditions a related Cauchy
problem possesses a unique classical solution and explain in which sense it
solves a rigorous formulation of the initial Ventsell problem. As a second
result we prove that functions that are intrinsically Lipschitz on the
snowflake boundary admit Euclidean Lipschitz extensions to the closure of the
entire domain. Our methods combine the fractal membrane analysis, the vector
analysis for local Dirichlet forms and PDE on fractals, coercive closed forms,
and the analysis of Lipschitz functions.
