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@article{AA_2018_30_2_a1,
author = {F. G. Avkhadiev},
title = {Integral inequalities of {Hardy} and {Rellich} in domains satisfying an exterior sphere condition},
journal = {Algebra i analiz},
pages = {18--44},
publisher = {mathdoc},
volume = {30},
number = {2},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AA_2018_30_2_a1/}
}
F. G. Avkhadiev. Integral inequalities of Hardy and Rellich in domains satisfying an exterior sphere condition. Algebra i analiz, Tome 30 (2018) no. 2, pp. 18-44. http://geodesic.mathdoc.fr/item/AA_2018_30_2_a1/
[1] Balinsky A. A., Evans W. D., Lewis R. T., The analysis and geometry of Hardy's inequality, Universitext, Springer, Heidelberg, 2015 | DOI | MR
[2] Matskewich T., Sobolevskii P. E., “The best possible constant in a generalized Hardy's inequality for convex domains in $\mathbb R^n$”, Nonlinear Anal., 28:9 (1997), 1601–1610 | DOI | MR
[3] Marcus M., Mitzel V. J., Pinchover Y., “On the best constant for Hardy's inequality in $\mathbb R^n$”, Trans. Amer. Math. Soc., 350:8 (1998), 3237–3250 | DOI | MR
[4] Davies E. B, “A review of Hardy inequalities”, The Maz'ya anniversary collection (Rostok, 1998), v. 2, Oper. Theory Adv. Appl., 110, Birkhäuser, Boston, 1999, 5–67 | MR
[5] Barbatis G., Filippas S, Tertikas A., “A unified approach to improved $L^p$ Hardy inequalities with best constants”, Trans. Amer. Math. Soc., 356:6 (2004), 2169–2196 | DOI | MR
[6] Avkhadiev F. G., “Hardy type inequalities in higher dimensions with explicit estimate of constants”, Lobachevskii J. Math., 21 (2006), 3–31 | MR | Zbl
[7] Avkhadiev F. G., “Neravenstva tipa Khardi v ploskikh i prostranstvennykh otkrytykh mnozhestvakh”, Tr. Mat. in-ta RAN, 255, 2006, 8–18 | MR
[8] Avkhadiev F. G., Shafigullin I. K., “Tochnye otsenki konstant Khardi dlya oblastei so spetsialnymi granichnymi svoistvami”, Izv. vuzov. Mat., 2014, no. 2, 69–73
[9] Avkhadiev F. G., Wirths K.-J., “Unified Poincaré and Hardy inequalities with sharp constants for convex domains”, ZAMM Z. Angew. Math. Mech., 87:8–9 (2007), 632–642 | DOI | MR
[10] Avkhadiev F. G., Wirths K.-J., “Sharp Hardy-type inequalities with Lamb's constants”, Bull. Belg. Math. Soc. Simon Stevin, 18:4 (2011), 723–736 | MR
[11] Avkhadiev F. G., Wirths K.-J., “On the best constants for the Brezis-Marcus inequalities in balls”, J. Math. Anal. Appl., 396:2 (2012), 473–480 | DOI | MR
[12] Avkhadiev F. G., Laptev A., “Hardy inequalities for nonconvex domains”, Around the Research of Vladimir Maz'ya, v. I, Int. Math. Ser. (N.Y.), 11, Springer, New York, 2010, 1–12 | DOI | MR
[13] Avkhadiev F. G., “Hardy inequalities in non-convex domains of the Euclidean space”, J. Anal., 23 (2015), 1–20 | MR
[14] Avkhadiev F. G., “Geometricheskoe opisanie oblastei, dlya kotorykh konstanta Khardi ravna $1/4$”, Izv. RAN. Ser. mat., 78:5 (2014), 3–26 | DOI | MR | Zbl
[15] Owen M. P., “The Hardy-Rellich inequality for polyharmonic operators”, Proc. Roy. Soc. Edinburgh Sect. A, 129:4 (1999), 825–839 | DOI | MR
[16] Avkhadiev F. G., “Hardy-Rellich inequalities in domains of the Euclidean space”, J. Math. Anal. Appl., 442:2 (2016), 469–484 | DOI | MR
[17] Avkhadiev F. G., “Integralnye neravenstva v oblastyakh giperbolicheskogo tipa i ikh primeneniya”, Mat. sb., 206:12 (2015), 3–28 | DOI | MR
[18] Avkhadiev F. G., Nasibullin R. G., “Neravenstva tipa Khardi v proizvolnykh oblastyakh s konechnym vnutrennim radiusom”, Sib. mat. zh., 55:2 (2014), 239–250 | MR
[19] Avkhadiev F. G., Shafigullin I. K., “Otsenki konstant Khardi pri trubchatom rasshirenii mnozhestv i v oblastyakh s konechnymi granichnymi momentami”, Mat. tr., 16:2 (2013), 3–12 | MR
[20] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR