Pré-Publication, Document De Travail Année : 2026

Nonlinear Kinetic Diffusion Equations with $p$-Growth

Résumé

We establish the local boundedness of (sub-)solutions to nonlinear kinetic diffusion equations with $p$-growth, where the kinetic p-Laplace equation is a prototypical example. A key ingredient is the derivation of kinetic Gagliardo-Nirenberg inequalities, where the Lebesgue norm of a function is estimated in terms of its transport and diffusive directions controlled in different Lebesgue spaces.

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hal-05621739 , version 1 (13-05-2026)

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Helge Dietert, Lukas Niebel, Rico Zacher. Nonlinear Kinetic Diffusion Equations with $p$-Growth. 2026. ⟨hal-05621739⟩
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