Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 75 | |
Number of page(s) | 25 | |
DOI | https://doi.org/10.1051/cocv/2024061 | |
Published online | 07 October 2024 |
Extremal functions for the critical Trudinger–Moser inequality with logarithmic Kernels
1
Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro Via Orabona 4, 70125 Bari, Italy
2
Institut für Mathematik, Goethe-Universität Frankfurt D-60629 Frankfurt am Main, Germany
* Corresponding author: silvia.cingolani@uniba.it
Received:
9
December
2023
Accepted:
7
August
2024
In this paper we study Moser–Trudinger type inequalities for some nonlocal energy functionals in presence of a logarithmic convolution potential, when the domain is a ball. In particular, we perform a blow-up analysis to prove existence of extremal functions in the borderline case of critical growth. Using this, we sharpen the results in [S. Cingolani and T. Weth J. London Math. Soc. 105 (2022) 1897–1935] under critical growth assumptions and give answers to some questions left open in [S. Cingolani and T. Weth J. London Math. Soc. 105 (2022) 1897–1935].
Mathematics Subject Classification: 35J50 / 35Q40 / 31A10
Key words: Trudinger–Moser inequality / logarithmic convolution potential / extremal functions / symmetry
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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