NONTRIVIAL SOLVABILITY OF ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH COMPLEX COEFFICIENTS

摘要

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.