Anisotropic Improved Leray-Trudinger Inequality

2025/06/19 by Giuseppina di Blasio, Di Blasio, Giuseppina, Giovanni Pisante +3
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.16167

Abstract

We establish a Leray- Trudinger Type inequality in the anisotropic setting induced by a strongly convex Finsler norm F. The result generalizes classical exponential integrability inequalities for Sobolev functions to the framework of anisotropic Sobolev spaces W^1,n₀(Ω), where the standard Euclidean norm is replaced by F and associated polar norm F^o. Moreover, in the class of anisotropically radial functions, we obtain the optimal constant in the spirit of Moser's sharp inequality.

Citations

• The optimal Leray-Trudinger inequality
• Eigenvalues of the Finsler p-Laplacian on varying domains
• A weighted anisotropic Sobolev type inequality and its applications to\n Hardy inequalities
• Finsler Hardy inequalities
• Optimal non-homogeneous improvements for the series expansion of Hardy's\n inequality
• An Improved Leray-Trudinger Inequality
• Anisotropic Hardy inequalities
• Trudinger–Moser type inequalities with logarithmic weights in dimension N
• A Leray-Trudinger Inequality
• Adams inequalities on measure spaces
• A unified approach to improved L^p Hardy inequalities with best constants

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• Anisotropic Moser-Trudinger inequality involving Lⁿ norm in the entire space ℝⁿ
• Sharp anisotropic singular Trudinger-Moser inequalities in the entire space
• Anisotropic Moser-Trudinger inequality involving Lⁿ norm
• Optimal concentration level of anisotropic Trudinger-Moser functionals on any bounded domain
• Weighted anisotropic Sobolev inequality with extremal and associated singular problems