Hardy-type inequality with double singular kernels

• Autorzy: Alexander Fabricant , Nikolai Kutev , Tsviatko Rangelov
• Języki publikacji: EN

Abstrakty

EN

A Hardy-type inequality with singular kernels at zero and on the boundary ∂Ω is proved. Sharpness of the inequality is obtained for Ω= B 1(0).

Słowa kluczowe

EN

Hardy inequality; Sharp estimates

Kategorie tematyczne

• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 9
• Strony: 1689-1697

Daty

wydano

2013-09-01

online

2013-06-28

Twórcy

autor

Alexander Fabricant

• Institute of Mathematics and Informatics

autor

Nikolai Kutev

• Institute of Mathematics and Informatics

autor

Tsviatko Rangelov

• Institute of Mathematics and Informatics

Bibliografia

• [1] Adimurthi, Chaudhuri N., Ramaswamy M., An improved Hardy-Sobolev inequality and its application, Proc. Amer. Math. Soc., 2002, 130(2), 489–505 http://dx.doi.org/10.1090/S0002-9939-01-06132-9
• [2] Alvino A., Volpicelli R., Volzone B., On Hardy inequalities with a remainder term, Ric. Mat., 2010, 59(2), 265–280 http://dx.doi.org/10.1007/s11587-010-0086-5
• [3] Brezis H., Marcus M., Hardy’s inequalities revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 1997, 25(1–2), 217–237
• [4] Brezis H., Vázquez J.L., Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Complut. Madrid, 1997, 10(2), 443–469
• [5] Filippas S., Tertikas A., Optimizing improved Hardy inequalities, J. Funct. Anal., 2002, 192(1), 186–233 http://dx.doi.org/10.1006/jfan.2001.3900
• [6] Ghoussoub N., Moradifam A., On the best possible remaining term in the Hardy inequality, Proc. Natl. Acad. Sci. USA, 2008, 105(37), 13746–13751 http://dx.doi.org/10.1073/pnas.0803703105
• [7] Gradsteyn I.S., Ryzhik I.M., Table of Integrals, Series and Products, Academic Press, New York, 1980
• [8] Maz’ja V.G., Sobolev Spaces, Springer Ser. Soviet Math., Springer, Berlin, 1985
• [9] Nazarov A.I., Dirichlet and Neumann problems to critical Emden-Fowler type equations, J. Global. Optim., 2008, 40(1–3), 289–303 http://dx.doi.org/10.1007/s10898-007-9193-6
• [10] Pinchover Y., Tintarev K., Existence of minimizers for Schrödinger operators under domain perturbations with application to Hardy’s inequality, Indiana Univ. Math. J., 2005, 54(4), 1061–1074 http://dx.doi.org/10.1512/iumj.2005.54.2705
• [11] Shen Y., Chen Z., Sobolev-Hardy space with general weight, J. Math. Anal. Appl., 2006, 320(2), 675–690 http://dx.doi.org/10.1016/j.jmaa.2005.07.044

Identyfikatory

DOI

10.2478/s11533-013-0260-6