In this paper, we derive explicit sharp two-sided estimates of the Dirichlet heat kernel for a class of symmetric subordinate diffusion processes with diffusive components in \(C^{1, \alpha }(\alpha \in (0, 1])\) open sets in \({\mathbb {R}}^d\) when the scaling order of the Laplace exponent of purely discontinuous part of the subordinator is between 0 and 1 including 1. The main result of this paper shows the stability of Dirichlet heat kernel estimates for such processes in \(C^{1, \alpha }\) open sets in the sense that the estimates depend on the divergence elliptic operator only via its uniform ellipticity constant and the Dini continuity modulus of the diffusion coefficients. As a corollary, we obtain sharp two-sided estimates for Green functions of those processes in bounded \(C^{1, \alpha }\) open sets.
