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We show interior H\"older continuity for a class of quasi-linear degeneratereaction-diffusion equations. The diffusion coefficient in the equation has aporous medium type degeneracy and its primitive has a singularity. The reactionterm is locally bounded except in zero. The class of equations we analyse ismotivated by a model that describes the growth of biofilms. Our method is basedon the original proof of interior H\"older continuity for the porous mediumequation. We do not restrict ourselves to solutions that are limits in the weaktopology of a sequence of approximate continuous solutions of regularizedproblems, which is a common assumption.

Interior H\"older continuity for singular-degenerate porous medium type equations with an application to a biofilm model