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arXiv · 2402.18572

Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations

Elie Abdo·Fizay-Noah Lee
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Abstract

We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states.

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Elie Abdo, Fizay-Noah Lee. 2024-02-28. Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations. https://arxiv.org/abs/2402.18572

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