Unique solvability of the stationary Fokker-Planck equation in a class of positive functions

摘要

We study the stationary Focker-Planck equation Δu - div(uf) = 0 with a given vector field f of the class C0∞(Rn) on the basis of a fixed point principle that generalizes the contraction mapping method. Next, we introduce a parameter in the equation and prove the unique solvability of the equation Δu - div(uγf) = 0 with the parameter in the class of positive slowly increasing functions. We reveal the analytic dependence of the positive solution u on the parameter γ. Pointwise estimates for positive solutions are proved. [PUBLICATION ABSTRACT]