Calculus of Variations and Geometric Measure Theory
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G. Bellettini - M. Novaga

Barriers for a Class of Geometric Evolutions Problems

created on 04 Dec 1996


Inserted: 4 dec 1996

Year: 1996


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 ut + F(t, x, grad u, grad2u) =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.

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