Barriers for a class of geometric evolution problems

Bellettini, Giovanni ; Novaga, Matteo

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 8 (1997) no. 2, pp. 119-128

Résumé

We present some general results on minimal barriers in the sense of De Giorgi for geometric evolution problems. We also compare minimal barriers with viscosity solutions for fully nonlinear geometric problems of the form \( u_{t} + F(t, x, \nabla u, \nabla^{2} u) = 0 \). If \( F \) is not degenerate elliptic, it turns out that we obtain the same minimal barriers if we replace \( F \) with \( F^{+} \), which is defined as the smallest degenerate elliptic function above \( F \).