Existence and non-existence of the first eigenvalue of the perturbed Hardy–Sobolev operator

By Adimurthi, K. Sandeep. Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2002

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Optimal Hardy–Rellich inequalities, maximum principle and related eigenvalue problem (2006, background): “In order to follow the same proofs as in [4], we need some test functions and their main properties will be proved in Appendix A.”
Optimizing Improved Hardy Inequalities (2002, result): “After this work was completed we learned that related results have been obtained in [ACR, AS ] by dierent methods.”
On a version of Trudinger–Moser inequality with Möbius shift invariance (2009, background): “B u2 |x|2(log 1/|x|)2 dx (for the Hardy inequality in dimension 2 see Adimurthi and Sandeep [2]).”