Extremal functions for the critical Trudinger-Moser inequality with logarithmic Kernels
Abstract. 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 [15] under critical growth assumptions and gives answers to some questions left open in [15].
Authors
- Silvia Cingolani (ORCID: https://orcid.org/0000-0002-3680-9106)
- Tobias Weth (ORCID: https://orcid.org/0000-0001-5347-8057)
- Meng Yu (ORCID: https://orcid.org/0009-0003-8065-4863)
Institutions
- Goethe University Frankfurt (DE)
- University of Bari Aldo Moro (IT)
Publication Details
- Journal
- ESAIM Control Optimisation and Calculus of Variations
- Published
- 2024-08-09
- DOI
- https://doi.org/10.1051/cocv/2024061
- Citations
- 2
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.72
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Deutscher Akademischer Austauschdienst
- China Scholarship Council
- Goethe-Universität Frankfurt am Main