https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/535 Sat, 04 Jul 2026 09:25:57 GMT 2026-07-04T09:25:57Z 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. Fri, 01 May 2026 00:00:00 GMT https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/213109 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. Wed, 01 Apr 2026 00:00:00 GMT https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/211006 2026-04-01T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/212406 Title: Convexity for a parabolic fully nonlinear free boundary problem with singular term Authors: Jeon, Seongmin; Shahgholian, Henrik Abstract: In this paper, we study a parabolic free boundary problem in an exterior domain {F(D(2)u) - partial derivative(t)u = u(chi{u>0})(a) in (R-n\K) x (0,infinity), u = u(0 )on {t=0}, |del u| = u = 0 on partial derivative Omega boolean AND (R(n )x (0,infinity)), u = 1 in K x [0,infinity). Here, a belongs to the interval (-1,0), K is a (given) convex compact set in R-n, Omega={u > 0} superset of K x (0,infinity) is an unknown set, and F denotes a fully nonlinear operator. Assuming a suitable condition on the initial value u(0), we prove the existence of a nonnegative quasiconcave solution to the aforementioned problem, which exhibits monotone non-decreasing behavior over time.; In this paper, we study a parabolic free boundary problem in an exterior domain (Formula presented.) Here, a belongs to the interval (-1,0), K is a (given) convex compact set in Rn, Ω={u>0}⊃K×(0,∞) is an unknown set, and F denotes a fully nonlinear operator. Assuming a suitable condition on the initial value u0, we prove the existence of a nonnegative quasiconcave solution to the aforementioned problem, which exhibits monotone non-decreasing behavior over time. Mon, 01 Dec 2025 00:00:00 GMT https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/212406 2025-12-01T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/211701 Title: The trajectory of teachers' multicultural transformation: an analysis of teachers' beliefs about mathematics as a school subject Authors: Song, Ryoon-Jin; Ju, Mi-Kyung Abstract: As schools have become ethnically, culturally, and linguistically diversified, multicultural mathematics education is emerging as the paradigm of school mathematics reform. When considering that an enacted curriculum is a set of beliefs put into action by a teacher, it is important to understand teachers' beliefs for the successful implementation of multicultural mathematics education. From this perspective, this research analyzed mathematics teachers' narratives to describe the multicultural transformation of their beliefs about mathematics as a school subject in the context of a multicultural mathematics teacher education course. The analysis shows that through the course participation, the teachers came to see mathematics as a cultural construct and challenged the Eurocentric perspective of mathematics. This change facilitated the teachers to seek ways to make school mathematics inclusive and equitable. The analysis also revealed the teachers' contradicting beliefs, which led them to engage in dialogues for collective reflection to nurture their narratives of multicultural mathematics education. The results of this research imply that a multicultural teacher education program should be extended into a community to support teachers' lifelong learning within a collaborative network of sharing and nurturing their narratives by integrating theory and practice about multicultural mathematics education. Sun, 01 Jun 2025 00:00:00 GMT https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/211701 2025-06-01T00:00:00Z