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2024 | OriginalPaper | Chapter

Improved Hardy Inequality with Logarithmic Term

Authors : Nikolai Kutev, Tsviatko Rangelov

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

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Abstract

New Hardy type inequality with double singular kernel and with additional logarithmic term in a ball \(B\subset {\text {I}}\!{\text {R}}^n\) is proved. As an application an estimate from below of the first eigenvalue for Dirichlet problem of p-Laplacian in a bounded domain \(\varOmega \subset {\text {I}}\!{\text {R}}^n\) is obtain.

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previous chapter On the Exact Solutions of a Sequence of Nonlinear Differential Equations Possessing Polynomial Nonlinearities

next chapter Robin Boundary Value Problem for Some Nonlinear Nonlocal Elliptic Partial Differential Equations

Barbatis, G., Filippas, S., Tertikas, A.: Series expansion for l \(^p\)hardy inequalities. Indiana Univ. Math. J. 52(1), 171–189 (2003)

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 (2003)

Belloni, M., Kawohl, B.: A direct uniqueness proof for equations involving the p-laplace operator. Manuscripta Math. 109, 229–231 (2002)

Benedikt, J., Drábek, P.: Estimates of the principal eigenvalue of the p-laplacian. J. Math. Anal. Appl. 393, 311–315 (2012)

Benedikt, J., Drábek, P.: Asymptotics for the principal eigenvalue of the p-laplacian on the ball as p approaches 1. Nonlinear Analysis 93, 23–29 (2013)

Biezuner, R., Brown, J., Ercole, G., Martins, E.: Computing the first eigenpair of the p-laplacian via the inverse iteration and sublinear supersolution. J. Sci. Comput. 52(1), 180–201 (2012)

Cheeger, J.: A lower bound for smallest eigenvalue of the laplacian. In: R.C. Gunning (ed.) Problems in Analysis, A Symposium in Honor of Salomon Bochner, pp. 195–199. Princeton Univ. Press (1970)

Fabricant, A., Kutev, N., Rangelov, T.: Hardy–type inequalities with weights. Serdica Math. J. 41(4), 493–512 (2015)

Fabricant, A., Kutev, N., Rangelov, T.: Lower estimate of the first eigenvalue of p-laplacian via hardy inequality. Compt. Rend. Acad. Sci. Bulgar. 68(5), 561–568 (2015)

10.

Kawohl, B., Fridman, V.: Isoperimetric estimates for the first eigenvalue of the p-laplace operator and the cheeger constant. Comment. Math. Univ. Carolinae 44(4), 659–667 (2003)

11.

Kutev, N., Rangelov, T.: Estimates from below for the first eigenvalue of the p–laplacian. AIP, Conference Proceedings 2159, 030,018–1–030,018–1 (2019)

12.

Kutev, N., Rangelov, T.: Lower estimate of the first eigenvalue of p-laplacian via hardy inequality. Compt. Rend. Acad. Sci. Bulgar. 72(9), 1167–1176 (2019)

13.

Kutev, N., Rangelov, T.: Hardy Inequalities and Applications: Inequalities with Double Singular Weight. Walter De Gruyter, Berlin (2022)

14.

Lefton, L., Wei, D.: Numerical approximation of the first eigenpair of the p-laplacian using finite elements and penalty method. Numer. Funct. Anal. Optim. 18, 389–399 (1997)

15.

Lindqvist, P.: On a nonlinear eigenvalue problem. Fall School Anal. Lect., Ber. Univ. Jyväskylä Math. Inst. 68, 33–54 (1995)

16.

Ludwig, M., Xiao, J., Zhang, G.: Sharp convex lorentz–sobolev inequalities. Math. Anal. 350, 169–197 (2011)

17.

Maz’ja, V.G.: Sobolev spaces. Springer Verlag, Berlin (1985)

18.

Ôtani, M.: A remark on certain nonlinear elliptic equations. Proc. Fac. Sci. Tokai Univ. 19, 23–28 (1984)

19.

Vladimirov, V.S.: Equations of Mathematical Physics. Marsel Dekker, New York (1971)

Title: Improved Hardy Inequality with Logarithmic Term
Authors: Nikolai Kutev
Tsviatko Rangelov
Publisher: Springer Nature Switzerland
Book: New Trends in the Applications of Differential Equations in Sciences
Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-53212-2_6

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