Smoothness of a boundary

Let fl C i be a bounded domain with a boundary L, = flUL, m = 2,3. The boundary T belongs to the class if there exist two real numbers b 0, h 0, p coordinate systems 

Here is the space of functions having k Lipschitz continuous deriva- 

Now consider a domain fl containing a surface Tc, whose properties are described in Section 1.1.7. Denote Sc = Tc clTc, flc = fl Tg. Introduce the unit normal n to Tc and define the opposite faces T of the surface Tg. The signs fit positive and negative directions of n, respectively. Then we denote the boundary of flc by dflc = T U T. We assume that there exists a closed extension S of Tc dividing the domain fl into two subdomains Di, D2 with boundaries dfli,dfl2 and such that Tc C S. It is assumed that = S , 80,2 = S+ U r. We say that the boundary dOc belongs to the class if 80,1,80,2 belong to G .  

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