On the best constant of Hardy–Sobolev inequalities

Brezis, 1997, Blow–up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Comp. Madrid, 10, 443 Brezis, 1997, Hardy’s inequality revisited, Ann. Sc. Norm. Pisa, 25, 217 Barbatis, 2003, Refined geometric Lp Hardy inequalities, Commun. Contemp. Math., 5, 869, 10.1142/S0219199703001166 Aubin, 1976, Probléme isopérimétric et espace de Sobolev, J. Differential Geom., 11, 573, 10.4310/jdg/1214433725 Talenti, 1976, Best constant in Sobolev inequality, Ann. Mat. Pura Appl., 110, 353, 10.1007/BF02418013 Maz’ya, 1985 Tertikas, 2007, On existence of minimizers for the Hardy–Sobolev–Maz’ya inequality, Ann. Mat. Pura Appl. (4), 186, 645, 10.1007/s10231-006-0024-z Benguria, 2008, The sharp constant in the Hardy–Sobolev–Maz’ya inequality in the three dimensional upper half space, Math. Res. Lett., 15, 613, 10.4310/MRL.2008.v15.n4.a1 G. Mancini, K. Sandeep, On a semilinear elliptic equation in Hn, preprint Filippas, 2002, Optimizing improved hardy inequalities, J. Funct. Anal., 192, 186, 10.1006/jfan.2001.3900 Caffarelli, 1984, First order interpolation inequalities with weights, Compos. Math., 53, 259 Catrina, 2001, On the Caffarelli–Kohn–Nirenberg inequalities: Sharp constants, existence (and nonexistence) and symmetry of extremal functions, Comm. Pure Appl. Math., LIV, 229, 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I Brezis, 1983, Positive solutions of nonlinear elliptic problems involving critical exponents, Comm. Pure Appl. Math., 36, 437, 10.1002/cpa.3160360405