*Published Paper*

**Inserted:** 4 dec 1996

**Last Updated:** 10 nov 2018

**Journal:** Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei, serie IX

**Volume:** VIII

**Number:** 2

**Pages:** 119-128

**Year:** 1997

**Abstract:**

We prove that the minimal barriers in the sense of De Giorgi are equivalent to the viscosity solutions for fully nonlinear parabolic geometric problems of the form $u_t + F(t, x,\nabla u, \nabla^2 u) =0$, under the assumptions on $F$ made by Giga-Goto-Ishii-Sato in a recent paper. More generally, we prove that the minimal barrier is the maximal between all viscosity subsolutions assuming a given initial datum. All results can be extended to the case in which $F$ is not degenerate elliptic, provided that also $F^+$, which is defined as the smallest degenerate elliptic function above $F$, satisfies the assumptions of Giga-Goto-Ishii-Sato.