https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/534 2026-07-24T09:38:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/218974 Title: Eventual regularity of the volume-preserving mean curvature flow in three and two dimensions Authors: 전성민 2026-06-19T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/213109 Title: Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem ☆ Authors: Dong, Hongjie; Jeon, Seongmin Abstract: In this paper, we study solutions u of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder Q+1 subset of Rn+1, where the coefficients are weighted by x alpha n, alpha is an element of (-infinity, 1). We establish higher-order boundary Schauder type estimates of x alpha nu under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with H & ouml;lder continuous coefficients. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. 2026-05-01T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/211006 Title: The free boundary for a superlinear system Authors: De Silva, Daniela; Jeon, Seongmin; Shahgholian, Henrik Abstract: In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional(Formula presented) but solutions can be also understood in an ad hoc viscosity way.First, we prove the optimal regularity of minimizers using a variational approach. Then, we apply a linearization technique to establish the C1,α[jls-end-space/]-regularity of the “flat” part of the free boundary via a viscosity method. Finally, for minimizing free boundaries, we extend this result to analyticity. 2026-04-01T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/218162 Title: The primitive curve complex for a handlebody Authors: Cho, Sangbum; Lee, Jung Hoon Abstract: A simple closed curve in the boundary surface of a handlebody is called primitive if there exists an essential disk in the handlebody whose boundary circle intersects the curve transversely in a single point. The primitive curve complex is then defined to be the full subcomplex of the curve complex for the boundary surface, spanned by the vertices of primitive curves. Given any two primitive curves, we construct a sequence of primitive curves from one to the other one satisfying a certain property. As a consequence, we prove that the primitive curve complex for the handlebody is connected. 2026-04-01T00:00:00Z