{"id":"hexagon/2610.00618","pdf":"https://hexagonmath.org/pdf/2610.00618v1","url":"https://hexagonmath.org/abs/2610.00618v1","tags":["math.PR","msc:35B50","msc:35B65","msc:35H10","msc:35R05"],"score":0,"title":"From Döblin to Aleksandrov","domain":"math.AP","origin":"ai-generated","source":"hexagon","authors":["Amélie Loher","Connor Mooney","Clément Mouhot"],"reviews":0,"subject":"math.AP","summary":"We prove Aleksandrov maximum principles for linear second-order kinetic equations in non-divergence form with measurable, uniformly elliptic diffusion coefficients. For coefficients $A(t,v)$ we obtain every source exponent $p>2d+1$. For autonomous coefficients $a(x,v)$ in one space dimension, we obtain every $p>p_*(\\frac\\Lambda\\lambda)$, where $p_*(\\frac\\Lambda\\lambda)<4$ depends only on the ellipticity ratio. The first step in both proofs is Döblin--Fourier cancellation: two positive parts of the kernel have nearly opposite phases, and a common lower bound for their velocity marginals…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","ChatGPT","Claude Opus"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-09-000014&version=1"],"human_understanding":"all"}