We study the parameter dependence of complex geodesics with prescribed boundary value and direction on bounded strongly linearly convex domains.As an important application, we present a quantitative relationship between the regularity of the pluricomplex Poisson kernel of such a domain, which is a solution to a homogeneous complex Monge-Amp`{e}re equation with boundary singularity, and that of the boundary of the domain. Our results improve considerably previous ones in this direction due to Chang-Hu-Lee and Bracci-Patrizio.
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