Survey reveals geometric links between Onofri's inequality and sharp Trudinger-Moser inequalities in two-dimensional domains, highlighting analytical insights for nonlocal energy functionals.
The present survey is devoted to results on Trudinger-Moser inequalities in two dimension. We give a brief overview of the history of these celebrated inequalities and, starting from the geometric problem that motivated Moser's original work, we discuss the connection between Onofri's inequality for the unit sphere and sharp inequalities on Euclidean domains. Finally, we present recent results and new insights into nonlocal interaction energy functionals in two dimension, involving logarithmic kernels.
No takes yet. Share an insight, caveat, or question.
Borgia et al. (2024) studied this question.