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Список литературы
|
|
| |
| 1. |
E. Gagliardo, “Ulteriori propriet`a di alcune classi di funzioni in pi`u variabili”, Ricerche Mat., 8 (1959), 24-51   |
| 2. |
L. Nirenberg, “On elliptic partial differential equations”, Ann. Sc. Norm. Super. Pisa. Sci. Fis. Mat. Ser. 3, 13 (1959), 115–162 |
| 3. |
О.В. Бесов, “Интегральные оценки дифференцируемых функций на нерегулярных областях”, Матем. сб., 201:12 (2010), 69–82   ; O.V. Besov, “Integral estimates for differentiable functions on irregular domains”, Sb. Math., 201:12 (2010), 1777–1790 |
| 4. |
V.G. Maz'ya, Sobolev Spaces, Springer, Berlin, 1985 |
| 5. |
A. Ancona, “On strong barriers and an inequality of Hardy for domains in $\mathbb{R}^n$”, J. London Math. Soc, 34:2 (2), 274–290 |
| 6. |
F.G. Avkhadiev, “Hardy type inequalities in higher dimensions with explicit estimate of constants”, Lobachevskii J. Math., 21 (2006), 3–31 |
| 7. |
A.A. Balinsky, W.D. Evans and R.T. Lewis, The Analysis and Geometry of Hardy's Inequality, Universitext, Springer, Heidelberg-New York-Dordrecht-London, 2015 |
| 8. |
Ф.Г. Авхадиев, “Интегральные неравенства в областях гиперболического типа и их применения”, Матем. сборник, 206:2 (2015), 3–28 ; F.G. Avkhadiev, “Integral inequalities in domains of hyperbolic type and their applications”, Sb. Math., 206:2 (2015), 1657–1681 |
| 9. |
Ф.Г. Авхадиев, “Конформно инвариантные неравенства”, Итоги науки и техн. Сер. Соврем. мат. и ее прил. Темат. обз., 142, 2017, 28–41 ; F.G. Avkhadiev, “Conformally invariant inequalities”, J. Math. Sci., 241:6 (2019), 672–685 |
| 10. |
F.G. Avkhadiev, “Euclidean maximum moduli of plane domains and their applications”, Complex Variables and Elliptic Equations, 64:11 (2019), 1869–1880 |
| 11. |
M. Ruzhansky, D. Suragan, Hardy Inequalities on Homogeneous Groups, Progress in Mathematics, 327, Birkhauser, 2019 |
| 12. |
D.W. Robinson, “Hardy and Rellich inequalities on the complement of convex sets”, J. Aust. Math. Soc., 108:1 (2020), 98–119 |
| 13. |
F. Avkhadiev, “Selected results and open problems on Hardy-Rellich and Poincaré-Friedrichs inequalities”, Anal. Math. Phys., 11 (2021), 134, 1–20 |
| 14. |
Ф.Г. Авхадиев, “Неравенства типа Харди, содержащие градиент функции расстояния”, Уфимск. матем. журн., 13:3 (2021), 3–16 ; F.G. Avkhadiev, “Hardy type inequalities involving gradient of distance function”, Ufa Math. J., 13:3 (2021), 3–16 |
| 15. |
L.V. Ahlfors, Conformal invariants, Topics in Geometric Function Theory, McGraw - Hill, New-York, 1973 |
| 16. |
H. Rademacher, “Über partielle und totale Differenzierbarkeit I”, Math. Ann., 89:4 (1919), 340–359 |
| 17. |
H. Federer, Geometric measure theory, Springer, New York, 1969 |
| 18. |
D.H. Armitage, U. Kuran, “The convexity and the superharmonicity of the signed distance function”, Proc. Amer. Math. Soc., 93:4 (1985), 598–600 |
| 19. |
C. Mantegazza, A.C. Mennucci, “Hamilton-Jacobi equations and distance functions on Riemannian manifolds”, Appl. Math. Optim., 47 (2003), 1–25 |
| 20. |
А.И. Назаров, С.В. Поборчий, Неравенство Пуанкаре и его приложения, учебное пособие, Изд-во С.-Петербургского ун-та, СПб., 2012 [A.I. Nazarov, S.V. Poborchii, Poincaré inequality and its application, St.-Petersburg Publ., St.-Petersburg, 2012 (in Russian)] |
| 21. |
F.G. Avkhadiev, K.-J. Wirths, Schwarz-Pick Type Inequalities, Birkhäuser Verlag, Basel-Boston-Berlin, 2009 |
| 22. |
A.F. Beardon, C. Pommerenke, “The Poincaré metric of plane domains”, J. London Math. Soc. (2), 18 (1978), 475–483 |
| 23. |
L. Carleson, T.W. Gamelin, Complex dynamics, Springer, New York, 1993 |
| 24. |
C. Pommerenke, “Uniformly perfect sets and the Poincaré metric”, Arch. Math., 32 (1979), 192–199 |
| 25. |
A. Golberg, T. Sugawa, M. Vuorinen, “Teichmüller's theorem in higher dimensions and its applications”, Comput. Methods Funct. Theory., 20:3-4 (2020), 539–558 |
| 26. |
F.G. Avkhadiev, “Hardy-Rellich inequalities in domains of the Euclidean space”, J. Math. Anal. Appl., 442 (2016), 469–484 |
