A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N
Analysis of PDEs
2025-01-27 v2
Abstract
In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball or the entire space. We also show that the extremal functions satisfy suitable Euler-Lagrange equations. When the domain is the entire space, such equation can be derived by N-Laplacian Schrodinger equation strongly coupled with a higher order fractional Poisson's equation. The results extends [16] to any dimension N bigger than 2.
Cite
@article{arxiv.2410.10013,
title = {A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N},
author = {Alessandro Cannone and Silvia Cingolani},
journal= {arXiv preprint arXiv:2410.10013},
year = {2025}
}