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We prove locally in time the existence of the unique smooth solution(including smooth interface) to the multidimensional free boundary problem forthe thin film equation in the case of partial wetting. We also obtain theSchauder estimates and solvability for the Dirichlet and the Neumann problemfor a linear degenerate parabolic equation of fourth order. The final expandedversion of this paper is available at AIMS Journals, Discrete and ContinuousDynamical Systems - A athttp://aimsciences.org/article/doi/10.3934/dcds.2017156

Classical solvability of the multidimensional free boundary problem for the thin film equation in the case of partial wetting