Hardy inequalities with non-standard remainder terms

Cianchi, Andrea; Ferone, Adele

doi:10.1016/j.anihpc.2007.05.003

Cianchi, Andrea ; Ferone, Adele

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 5, pp. 889-906

EuDML MR Zbl

DOI : 10.1016/j.anihpc.2007.05.003

@article{AIHPC_2008__25_5_889_0,
     author = {Cianchi, Andrea and Ferone, Adele},
     title = {Hardy inequalities with non-standard remainder terms},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {889--906},
     year = {2008},
     publisher = {Elsevier},
     volume = {25},
     number = {5},
     doi = {10.1016/j.anihpc.2007.05.003},
     mrnumber = {2457816},
     zbl = {1153.26310},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.05.003/}
}

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Cianchi, Andrea; Ferone, Adele. Hardy inequalities with non-standard remainder terms. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 5, pp. 889-906. doi: 10.1016/j.anihpc.2007.05.003

Bibliographie
Cité par

[1] Adams R.A., Sobolev Spaces, Academic Press, Orlando, 1975. | Zbl | MR

[2] Adimurthi , Chaudhuri N., Ramaswamy M., An improved Hardy-Sobolev inequality and its applications, Proc. Amer. Math. Soc. 130 (2002) 489-505. | Zbl | MR

[3] Adimurthi , Esteban M.J., An improved Hardy-Sobolev inequality in $W^{1, p}$ and its applications to Schrödinger operators, NoDEA Nonlin. Differential Equation Appl. 12 (2005) 243-263. | Zbl | MR

[4] Barbatis G., Filippas S., Tertikas A., A unified approach to improved $L^{p}$ Hardy inequalities with best constants, Trans. Amer. Math. Soc. 356 (2004) 2169-2196. | Zbl | MR

[5] Bartsch T., Weth T., Willem M., A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator, Calc. Var. Part. Diff. Eq. 18 (2003) 57-75. | Zbl | MR

[6] Bennett C., Sharpley R., Interpolation of Operators, Academic Press, Boston, 1988. | Zbl | MR

[7] Bianchi G., Egnell H., A note on the Sobolev inequality, J. Funct. Anal. 100 (1991) 18-24. | Zbl | MR

[8] Brezis H., Lieb E., Sobolev inequalities with remainder terms, J. Funct. Anal. 62 (1985) 73-86. | Zbl | MR

[9] Brezis H., Marcus M., Shafrir I., Extremal functions for Hardy's inequality with weights, J. Funct. Anal. 171 (2000) 177-191. | Zbl | MR

[10] Brezis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983) 437-477. | Zbl | MR

[11] Brezis H., Wainger S., A note on limiting cases of Sobolev embeddings and convolution inequalities, Comm. Part. Diff. Eq. 5 (1980) 773-789. | Zbl | MR

[12] Brothers J.E., Ziemer W.P., Minimal rearrangements of Sobolev functions, J. Reine Angew. Math. 384 (1988) 419-431. | Zbl | MR

[13] Cianchi A., A quantitative Sobolev inequality in BV, J. Funct. Anal. 237 (2006) 466-481. | Zbl | MR

[14] A. Cianchi, Sharp Morrey-Sobolev inequalities and the distance from extremals, Trans. Amer. Math. Soc., in press. | Zbl | MR

[15] A. Cianchi, A. Ferone, A strenghtened version of the Hardy-Littlewood inequality, preprint. | Zbl

[16] A. Cianchi, N. Fusco, F. Maggi, A. Pratelli, The sharp Sobolev inequality in quantitative form, preprint. | MR

[17] Cwikel M., Pustylnik E., Sobolev type embeddings in the limiting case, J. Fourier Anal. Appl. 4 (1998) 433-446. | Zbl | MR

[18] Detalla A., Horiuchi T., Ando H., Missing terms in Hardy-Sobolev inequalities and its applications, Far East J. Math. Sci. 14 (2004) 333-359. | Zbl | MR

[19] Dolbeault J., Esteban M.J., Loss M., Vega L., An analytical proof of Hardy-like inequalities related to the Dirac operator, J. Funct. Anal. 216 (2004) 1-21. | Zbl | MR

[20] Edmunds D.E., Kerman R.A., Pick L., Optimal Sobolev imbeddings involving rearrangement invariant quasi-norms, J. Funct. Anal. 170 (2000) 307-355. | Zbl | MR

[21] N. Fusco, F. Maggi, A. Pratelli, The sharp quantitative Sobolev inequality in BV, preprint.

[22] Filippas S., Maz'Ya V.G., Tertikas A., On a question of Brezis and Marcus, Calc. Var. Part. Diff. Eq. 25 (2006) 491-501. | Zbl | MR

[23] Gazzola F., Grunau H.C., Mitidieri E., Hardy inequalities with optimal constants and remainder terms, Trans. Amer. Math. Soc. 356 (2004) 2149-2168. | Zbl | MR

[24] Gazzola F., Grunau H.C., Squassina M., Existence and non-existence results for critical growth biharmonic elliptic equations, Calc. Var. Part. Diff. Eq. 18 (2003) 117-143. | MR

[25] Hansson K., Imbedding theorems of Sobolev type in potential theory, Math. Scand. 45 (1979) 77-102. | Zbl | MR

[26] Kawohl B., Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math., vol. 1150, Springer-Verlag, Berlin, 1985. | Zbl | MR

[27] Maz'Ya V.G., Sobolev Spaces, Springer-Verlag, Berlin, 1985. | Zbl | MR

[28] Opic B., Kufner A., Hardy-type Inequalities, Longman Scientific Technical, Harlow, 1990. | Zbl | MR

[29] Pohozhaev S.I., On the imbedding Sobolev theorem for $p l = n$ , in: Doklady Conference, Section Math., Moscow Power Inst., 1965, pp. 158-170, (Russian).

[30] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976) 353-372. | Zbl | MR

[31] Tidblom J., A Hardy inequality in the half-space, J. Funct. Anal. 221 (2005) 482-495. | Zbl | MR

[32] Trudinger N.S., On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967) 473-483. | Zbl | MR

[33] Vazquez J.L., Zuazua E., The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, J. Funct. Anal. 173 (2000) 103-153. | Zbl | MR

[34] Yudovich V.I., Some estimates connected with integral operators and with solutions of elliptic equations, Soviet Math. Dokl. 2 (1961) 746-749. | Zbl

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