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Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture. / Nasibullin, Ramil; Gabdulkhalikov, Il’yas.

в: Analysis and Mathematical Physics, Том 16, № 4, 72, 04.06.2026.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Nasibullin, R & Gabdulkhalikov, I 2026, 'Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture', Analysis and Mathematical Physics, Том. 16, № 4, 72. https://doi.org/10.1007/s13324-026-01201-x

APA

Nasibullin, R., & Gabdulkhalikov, I. (2026). Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture. Analysis and Mathematical Physics, 16(4), [72]. https://doi.org/10.1007/s13324-026-01201-x

Vancouver

Nasibullin R, Gabdulkhalikov I. Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture. Analysis and Mathematical Physics. 2026 июнь 4;16(4):72. doi: 10.1007/s13324-026-01201-x

Author

Nasibullin, Ramil ; Gabdulkhalikov, Il’yas. / Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture. в: Analysis and Mathematical Physics. 2026 ; Том 16, № 4.

BibTeX

@article{1769b8e104b5416fbae6d066e1f4d351,
title = "Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture",
abstract = "This paper is devoted to Hardy type inequalities with additional terms. New one-dimensional inequalities are established. Using these one-dimensional inequalities, we obtain spatial inequalities for compactly supported smooth functions in n-balls with finite Dirichlet integral. We improve known lower estimates of the Brezis-Marcus constants for the Avkhadiev–Wirths conjecture and thus come closer to confirming the conjecture. The key point of the proofs of all the main results is the choice of special functions with parameters that are not dictated by anything.",
keywords = "Additional term, Distance function, Hardy inequality, Inner radius, Sharp constant",
author = "Ramil Nasibullin and Il{\textquoteright}yas Gabdulkhalikov",
note = "Nasibullin, R., Gabdulkhalikov, I. Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture. Anal.Math.Phys. 16, 72 (2026). https://doi.org/10.1007/s13324-026-01201-x The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2025-349 from 29.04.2025 with the Ministry of Science and Higher Education of the Russian Federation.",
year = "2026",
month = jun,
day = "4",
doi = "10.1007/s13324-026-01201-x",
language = "English",
volume = "16",
journal = "Analysis and Mathematical Physics",
issn = "1664-2368",
publisher = "Springer",
number = "4",

}

RIS

TY - JOUR

T1 - Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture

AU - Nasibullin, Ramil

AU - Gabdulkhalikov, Il’yas

N1 - Nasibullin, R., Gabdulkhalikov, I. Improved Brezis-Marcus constants for Avkhadiev–Wirths conjecture. Anal.Math.Phys. 16, 72 (2026). https://doi.org/10.1007/s13324-026-01201-x The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2025-349 from 29.04.2025 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2026/6/4

Y1 - 2026/6/4

N2 - This paper is devoted to Hardy type inequalities with additional terms. New one-dimensional inequalities are established. Using these one-dimensional inequalities, we obtain spatial inequalities for compactly supported smooth functions in n-balls with finite Dirichlet integral. We improve known lower estimates of the Brezis-Marcus constants for the Avkhadiev–Wirths conjecture and thus come closer to confirming the conjecture. The key point of the proofs of all the main results is the choice of special functions with parameters that are not dictated by anything.

AB - This paper is devoted to Hardy type inequalities with additional terms. New one-dimensional inequalities are established. Using these one-dimensional inequalities, we obtain spatial inequalities for compactly supported smooth functions in n-balls with finite Dirichlet integral. We improve known lower estimates of the Brezis-Marcus constants for the Avkhadiev–Wirths conjecture and thus come closer to confirming the conjecture. The key point of the proofs of all the main results is the choice of special functions with parameters that are not dictated by anything.

KW - Additional term

KW - Distance function

KW - Hardy inequality

KW - Inner radius

KW - Sharp constant

UR - https://www.scopus.com/pages/publications/105040993659

UR - https://www.mendeley.com/catalogue/02be2300-6c72-3571-a20d-e5f88fe33d31/

U2 - 10.1007/s13324-026-01201-x

DO - 10.1007/s13324-026-01201-x

M3 - Article

VL - 16

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

SN - 1664-2368

IS - 4

M1 - 72

ER -

ID: 80150792