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arXiv · 2506.16167

Anisotropic Improved Leray-Trudinger Inequality

Giuseppina Di Blasio·Giovanni Pisante·Georgios Psaradakis
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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 $W^{1,n}_0(\Omega)$, 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.

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Giuseppina Di Blasio, Giovanni Pisante, Georgios Psaradakis. 2025-06-19. Anisotropic Improved Leray-Trudinger Inequality. https://arxiv.org/abs/2506.16167

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