A Mixed Type Generalized Kimura Operator

TL;DR

This paper studies a class of mixed type generalized Kimura operators on 2D manifolds with corners, providing analysis, estimates, and proofs of existence and regularity of solutions and heat kernels, with applications to topological insulators.

Contribution

It introduces a new analysis framework for mixed type Kimura operators on manifolds with corners, including estimates and existence proofs for solutions and heat kernels.

Findings

Established degenerate H"older space estimates for model operators

Proved existence and regularity of solutions to the operators

Demonstrated the existence and regularity of the global heat kernel

Abstract

We analyze a class of mixed type generalized Kimura operators on 2-dimensional compact manifolds with corners that find applications in the analysis of topological insulators. We model the operator and provide the degenerate H\"older space-type estimates for model operators. With the analysis of perturbation term we establish the existence of solutions. We also give proofs of the existence and regularity of the global heat kernel.