A Mixed Type Generalized Kimura Operator

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.