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Barriers for a class of geometric evolution problems. (English) Zbl 0990.35070
Minimal barriers have been introduced by De Giorgi in order to provide a notion of weak solution for partial differential equations as, for example, the mean curvature flow, which is suitable to describe the evolution even past singularities. In this note the authors announce general results on minimal barriers and theorems comparing minimal barriers and viscosity solutions which are proved in [J. Differ. Equations 139, 76-103 (1997; Zbl 0882.35028), and Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4) 26, 97-131 (1998; Zbl 0904.35041)]. For details see the corresponding reviews.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
49Q20 Variational problems in a geometric measure-theoretic setting
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