Nontrivial solvability of elliptic equations in divergence form with complex coefficients

A. I. Noarov

Institute of Numerical Mathematics, Moscow, Russia

Abstract: The stationary Fokker–Planck–Kolmogorov equation with complex diffusion coefficients and a complex vector-field is examined on a torus. Under suitable conditions for the diffusion coefficients, it is proven that a nontrivial solution exists and the solution space is multidimensional in some cases.

Keywords: stationary Fokker–Planck–Kolmogorov equation, Weyl decomposition.

UDC: 517.956.22

Received: 25.06.2013

 English version: Siberian Mathematical Journal, 2014, 55:3, 465–470

Bibliographic databases:

• 
• 
• 
• 
•