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We construct new optimal 
$L^{p}$ Hardy-type inequalities for elliptic Schrödinger-type operators with a potential term.
Let Ω be an open connected cone in ℝn 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.
