A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N

Alessandro Cannone; Silvia Cingolani

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arXiv · 2410.10013

A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N

Alessandro Cannone·Silvia Cingolani

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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.

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Alessandro Cannone, Silvia Cingolani. 2024-10-13. A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N. https://arxiv.org/abs/2410.10013

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