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In this paper we are dealing with two classes of mean curvature type problemsthat generalize the translating soliton problem. A first result proves that thesolutions to these problems have unique interior critical points. Using thisuniqueness result, we next derive a priori $C^0$ and $C^1$ estimates for thesolutions to these problems, by means of some minimum principles forappropriate $P$-functions, in the sense of L.E. Payne.

Minimum principles and a priori estimates for some translating soliton type problems