Well-posedness of a free boundary problem of early atherosclerotic plaque formation with reverse cholesterol transport

Atherosclerosis, a chronic inflammatory disease that originates from a plaque that forms in the artery, is a leading cause of disability and premature death in the world. In this paper, we consider a free boundary model of early atherosclerotic plaque formation under the influence of reverse cholesterol transport (RCT), which includes low-density lipoprotein (LDL), high-density lipoprotein (HDL), endothelial stimulating cytokines, macrophages and foam cells. For this model, we first reduce the free boundary to a fixed boundary by using the Hanzawa transformation, and then prove the existence and uniqueness of the solution in suitable Hölder spaces by using the theory of analytic semigroups. Our main novelty is to reduce the regional regularity requirement for the corresponding problem from m ≥ 4 to m ≥ 3 with respect to (J. Math. Anal. Appl., 2022, Paper No. 125606).