Weak and Perron Solutions for Stationary Kramers-Fokker-Planck Equations in Bounded Domains

Benny Avelin; Mingyi Hou

Weak and Perron Solutions for Stationary Kramers-Fokker-Planck Equations in Bounded Domains

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2405.04070 v3 pith:UOVFGXYM submitted 2024-05-07 math.AP

Benny Avelin , Mingyi Hou This is my paper · ORCID

classification math.AP

keywords solutionsdomainsweakboundedequationsexistencekramers-fokker-planckperron-wiener-brelot

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original abstract

In this paper, we investigate weak solutions and Perron-Wiener-Brelot solutions to the linear stationary Kramers-Fokker-Planck equation in bounded domains. We establish the existence of weak solutions in product domains by applying the Lions-Lax-Milgram theorem and the vanishing viscosity method. Furthermore, we show that these solutions coincide in well-behaved domains. Building on the existence of weak solutions in product domains, we develop the foundational theory of Perron-Wiener-Brelot solutions in arbitrary bounded domains. Our results rely on recent advancements in the theory of kinetic Fokker-Planck equations with rough coefficients.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Gradient estimates for nonlinear kinetic Fokker-Planck equations
math.AP 2025-02 conditional novelty 8.0 of 10

For nonlinear kinetic Fokker-Planck equations, the velocity gradient is controlled pointwise by kinetic Riesz potentials of the data, yielding new Hölder, BMO, and Calderón-Zygmund regularity criteria.

Pith tools