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

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