Convexity for a parabolic fully nonlinear free boundary problem with singular term

초록

In this paper, we study a parabolic free boundary problem in an exterior domain (Formula presented.) Here, a belongs to the interval (-1,0), K is a (given) convex compact set in Rn, Ω={u>0}⊃K×(0,∞) is an unknown set, and F denotes a fully nonlinear operator. Assuming a suitable condition on the initial value u0, we prove the existence of a nonnegative quasiconcave solution to the aforementioned problem, which exhibits monotone non-decreasing behavior over time.

키워드