Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator

Charles L. Epstein, Jon Wilkening

We study the classical Kimura diffusion operator defined on the n-simplex, $$L^{Kim}=\sum _{1\le i,j\le n+1}{x}_i{x}_j{\partial }_{x_i}{\partial }_{x_j}$$ We give novel constructions for th…