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arXiv · 1508.01482

Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator

Charles L. Epstein·Jon Wilkening
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Abstract

We study the classical Kimura diffusion operator defined on the n-simplex, $$L^{Kim}=\sum_{1\leq i,j\leq n+1}x_ix_j\partial_{x_i}\partial_{x_j}$$ We give novel constructions for the basis of eigenpolynomials, and the solution to the inhomogeneous Dirichlet problem, which are well adapted to numerical applications. Our solution of the Dirichlet problem is quite explicit and provides a precise description of the singularities that arise along the boundary.

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Charles L. Epstein, Jon Wilkening. 2015-08-06. Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator. https://arxiv.org/abs/1508.01482

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