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Sharp Hardy-Sobolev inequalities. (English) Zbl 1058.26007

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.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
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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
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