A Geometrical Version of Hardy's Inequality

By M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, Ari Laptev. 2002

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On a question of Brezis and Marcus (2006, background): “This question was answered in affirmative in [11] for p = 2 and later in [16] for any p > 1.”
Critical Hardy–Sobolev inequalities (2006, methodology): “ 1.1 a crucial step is to obtain local estimates in a neighborhood of K, see Theorem 5.1. For other directions in improving Hardy inequalities we refer to [AE], [BV], [BFT], [BM], [CM], [DELV], [GP], [HHL], [M], [MMP], [Ti1], [Ti2], [VZ] and references therein. The paper is organized as follows. In ”
On the structure of Hardy–Sobolev–Maz'ya inequalities (2008, result): “This result has been improved and generalized in many different ways: see for example [1], [2], [4]–[9], [12], [13].”
A Hardy inequality in the half-space (2005, result): “Some results concerning a type of Hardy inequality involving the distance to the boundary were obtained in [1], [3], [ 7 ] and [11].”
Sharp Hardy-type inequalities with Lamb's constant (2011, background): “Laptev [10] for a generalization to convex domains of finite volume).”
Hardy-Sobolev-Maz'ya inequalities for arbitrary domains (2011, background): “6) was proved in [16]; see also [9, 1] for further developments.”