V. Barbu

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20242026

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math.PR2026

Uniqueness for nonlinear Fokker-Planck equations with general diffusion terms and their associated nonlinear Markov processes

Viorel Barbu, Yuqi Li, Michael RÃ¶ckner

This work is concerned with the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with non-diagonal diffusion terms of type \begin{equation} u_{t}-\sum_{i…

math.PR2025

The Leibenson process

Viorel Barbu, Sebastian Grube, Marco Rehmeier +1

Consider the Leibenson equation \begin{equation*} \partial_t u = Î_p u^q, \end{equation*} where $I^_{p} f = d i v (∣\nabla f ∣^{p - 2} \nabla f)$ for $p > 1$ and $q > 0$ , which is a simultaneo…

math.PR2025

Nonlinear Fokker-Planck equations as smooth Hilbertian gradient flows

Viorel Barbu, Michael RÃ¶ckner

Under suitable assumptions on $I^^{2} : R \to R, D : R^{d} \to R^{d}$ and $b : R^{d} \to R$ , the nonlinear Fokker-Planck equation $u_t…

math.PR2024

$p$ -Brownian motion and the $p$ -Laplacian

Viorel Barbu, Marco Rehmeier, Michael RÃ¶ckner

In this paper we construct a stochastic process, more precisely, a (nonlinear) Markov process, which is related to the parabolic $p$ -Laplace equation in the same way as Brownian mo…

Uniqueness for nonlinear Fokker-Planck equations with general diffusion terms and their associated nonlinear Markov processes

The Leibenson process

Nonlinear Fokker-Planck equations as smooth Hilbertian gradient flows

p-Brownian motion and the p-Laplacian

$p$ -Brownian motion and the $p$ -Laplacian