Barrier solutions (Q2717346)

The aim of the author is to study the theory of De Giorgi's barriers, in particular he is interested in geometric evolutions of sets.NEWLINENEWLINENEWLINEIn this case \textit{G. Bellettini} and \textit{M. Novaga} showed [Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4) 26, No. 1, 97-131 (1998; Zbl 0904.35041)] that the theory of barriers and the viscosity theory define the same weak solutions under general hypothesis on geometric evolutions.NEWLINENEWLINENEWLINEIn this note the definitions of interior and external barriers and some basic properties of them are given. Then the theory of barriers is applied to ordinary differential equations and systems of equations, later to partial differential equations of parabolic type. The author also gives the definition of solutions of barrier type. As a particular case geometric evolution equations are considered.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00026].