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We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary ÃŽÂ“1Ã‰Â›. It is assumed that ÃŽÂ“1Ã‰Â› consists of (1/ÃŽÂ´)nÃ¢ÂˆÂ’1 pieces with diameter of order O(Ã‰Â›ÃŽÂ´). In addition, ÃŽÂ´=ÃŽÂ´(Ã‰Â›) and ÃŽÂ´Ã¢Â†Â’0 as Ã‰Â›Ã¢Â†Â’0

journal of inequalities and applications

On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure