Kinetic Aleksandrov estimates
A Lean 4 / Mathlib formalisation of Aleksandrov maximum principles for kinetic equations d_t u + v.grad_x u - A : D_v^2 u = f in non-divergence form, with measurable, uniformly elliptic diffusion acting only in the velocity. For coefficients A(t,v) the estimate holds for every source exponent p > 2d+1; for autonomous coefficients a(x,v) in one space dimension for every p above a threshold 1 + beta_*(Lambda/lambda) = 1 + 128 d^2 (Lambda/lambda)^2 / 3. In each case the estimate implies interior Hölder continuity of solutions; for coefficients A(t,x,v) this is the kinetic Krylov–Safonov…
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