Best Constants for Anisotropic Moser-Trudinger Inequalities with the Exact Growth Condition and Their Applications
Abstract
We investigate the best constants associated with several types of Moser--Trudinger inequalities within the framework of the Finsler metric in ℝn. By employing a convex-symmetrization-free approach, we first establish both the critical and subcritical anisotropic singular Moser--Trudinger inequalities. We further study anisotropic Moser--Trudinger inequalities in both singular and nonsingular cases under the exact growth condition, highlighting the optimality of the best constant as well as the sharp exponent appearing in the denominator. To further enrich the theory, we introduce quasi-conformal-type transformations adapted to the Finsler metric setting to derive several new variants of such inequalities. We also characterize the attainability and nonattainability of maximizers for a generalized version of anisotropic Moser--Trudinger inequalities with the exact growth and explicitly determine the corresponding supremum values. As an application of these inequalities, we analyze the existence and nonexistence of positive ground state solutions to a class of n-Finsler-Laplace equations involving constant potential in ℝn, where the nonlinearity exhibits a critical exponential growth at infinity.
Related
- Unique Positive Extremals and Sharp Stability Constants for Singular Moser-Trudinger Inequalities
- Extremals and Thresholds for Critical Singular Anisotropic Moser-Trudinger Inequalities
- On sharp singular Moser-Trudinger type inequalities and applications to zero mass (p,Q)-Laplace subelliptic equations in the Heisenberg group
- Classification of solutions to the Liouville equation with a nonlinear Neumann boundary condition and applications to sharp inequalities
- Fractional and anisotropic Gagliardo--Nirenberg inequalities with applications
BibTeX
@misc{figueiredo2026best,
title = {{Best Constants for Anisotropic Moser-Trudinger Inequalities with the Exact Growth Condition and Their Applications}},
author = {Giovany M. Figueiredo and Deepak Kumar Mahanta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12260},
eprint = {2610.12260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12260},
}
RIS
TY - UNPB
TI - Best Constants for Anisotropic Moser-Trudinger Inequalities with the Exact Growth Condition and Their Applications
AU - Giovany M. Figueiredo
AU - Deepak Kumar Mahanta
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12260
UR - https://arxiv.org/abs/2610.12260
AB - We investigate the best constants associated with several types of Moser--Trudinger inequalities within the framework of the Finsler metric in ℝ^n. By employing a convex-symmetrization-free approach, we first establish both the critical and subcritical anisotropic singular Moser--Trudinger inequalities. We further study anisotropic Moser--Trudinger inequalities in both singular and nonsingular cases under the exact growth condition, highlighting the optimality of the best constant as well as the sharp exponent appearing in the denominator. To further enrich the theory, we introduce quasi-conformal-type transformations adapted to the Finsler metric setting to derive several new variants of such inequalities. We also characterize the attainability and nonattainability of maximizers for a generalized version of anisotropic Moser--Trudinger inequalities with the exact growth and explicitly determine the corresponding supremum values. As an application of these inequalities, we analyze the existence and nonexistence of positive ground state solutions to a class of n-Finsler-Laplace equations involving constant potential in ℝ^n, where the nonlinearity exhibits a critical exponential growth at infinity.
ER -