Eigenfunctions and the Dirichlet Problem for the Classical Kimura Diffusion Operator
Eigenfunctions and the Dirichlet Problem for the Classical Kimura Diffusion Operator
We study the classical Kimura diffusion operator defined on the $n$-simplex, $\operatorname{L^{Kim}}=\sum_{1\leq i,j\leq n+1}x_i(\delta_{ij}-x_j)\partial_{x_i}\partial_{x_j},$ which has important applications in population genetics. Because it is a degenerate elliptic operator acting on a singular space, special tools are required to analyze and construct solutions to elliptic and parabolic problems defined by this …