Optimal Hardy inequalities in cones - Devyver, Baptiste; Pinchover, Yehuda; Psaradakis, Georgios (Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2017)
Let Ω be an open connected cone in ℝ n with vertex at the origin. Assume that the Operator is subcritical in Ω, where δΩ is the distance function to the boundary of Ω and μ ⩽ 1/4. We show that under some smoothness assumption on Ω the improved Hardy-type inequality holds true, and the Hardy-weight λ(μ)|x|–2 is optimal in a certain definite sense. The constant λ(μ) > 0 is given explicitly.