Filippas, S.; Maz’ya, V. G.; Tertikas, A. Sharp Hardy-Sobolev inequalities. (English) Zbl 1058.26007 C. R., Math., Acad. Sci. Paris 339, No. 7, 483-486 (2004). Summary: Let \(\Omega\) be a smooth bounded domain in \(\mathbb R^N\), \(N\geqslant3\). We show that Hardy’s inequality involving the distance to the boundary, with best constant (1/4), may still be improved by adding a multiple of the critical Sobolev norm. Cited in 30 Documents MSC: 26D10 Inequalities involving derivatives and differential and integral operators Keywords:Hardy-Sobolev inequality; critical Sobolev norm PDFBibTeX XMLCite \textit{S. Filippas} et al., C. R., Math., Acad. Sci. Paris 339, No. 7, 483--486 (2004; Zbl 1058.26007) Full Text: DOI References: [1] Barbatis, G.; Filippas, S.; Tertikas, A., A unified approach to improved \(L^p\) Hardy inequalities with best constants, Trans. Amer. Math. Soc., 356, 6, 2169-2196 (2004) · Zbl 1129.26019 [2] Brezis, H.; Marcus, M., Hardy’s inequalities revisited, Ann. Scuola Norm. Pisa, 25, 217-237 (1997) · Zbl 1011.46027 [3] Dávila, J.; Dupaigne, L., Hardy-type inequalities, J. Eur. Math. Soc., 6, 3, 335-365 (2004) · Zbl 1083.26012 [4] S. Filippas, V.G. Maz’ya, A. Tertikas, Critical Hardy Sobolev inequalities, in preparation; S. Filippas, V.G. Maz’ya, A. Tertikas, Critical Hardy Sobolev inequalities, in preparation [5] Filippas, S.; Tertikas, A., Optimizing improved Hardy inequalities, J. Funct. Anal., 192, 186-233 (2002) · Zbl 1030.26018 [6] Maz’ya, V. G., Sobolev Spaces (1985), Springer · Zbl 0727.46017 [7] Vázquez, J. L.; Zuazua, E., The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, J. Funct. Anal., 173, 103-153 (2000) · Zbl 0953.35053 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.