Characterizations to the fractional Sobolev inequality

Published 11 Dec 2013 in math.CA and math.FA | (1312.3135v1)

Abstract: We characterize the fractional Sobolev inequality with fractional isocapacitary and isoperimetric inequalities. We give a sufficient condition and examples so that the fractional capacity of the closure of an open set is bounded above by the fractional perimeter of its interior.

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