The research monograph by Epstein and Mazzeo establishes the analytic regularity theory for a class of second order elliptic partial differential operators, called generalized Kimura operators, that arise in population biology, when looking at the diffusion approximation of Markov chains of Wright-Fisher type modelling the evolution of (finitely many) gene frequencies within populations undergoing genetic drift, mutation, selection and migration. Since only the absolute or relative distribution of types of genes matter, these operators are defined on orthants or simplices, hence domains with corners. As the variance in the genetic drift typically is proportional to the population size, the diffusion coefficients degenerate of order 1 at the boundary of the domain.
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