Analysis, PDE & Probability Seminar

Upcoming Seminars

2026. 2. 23 (Mon) 16:00-17:00  Room 1423
Hyungsung Yun (Changwon National University)

Boundary Hölder gradient estimates for fully nonlinear degenerate or singular parabolic equations

ABSTRACT. In this talk, we study the boundary regularity of viscosity solutions to fully nonlinear degenerate or singular parabolic equations of the form $$u_t = |Du|^\gamma F(D^2u)+f, \quad \gamma>-1.$$ The gradient-dependent degeneracy or singularity, together with the time derivative, poses significant difficulties compared to the elliptic case. We establish boundary $C^{1,\alpha}$ estimates for the Dirichlet problem under suitable structural assumptions on the operator and boundary data. The proof combines compactness arguments, barrier constructions, regularization techniques, and the boundary regularity of small perturbation solutions, together with the analysis of a model problem on a flat boundary. Our results unify and extend previous boundary regularity results and also provide a framework for studying boundary behavior in a broader class of nonlinear parabolic equations.

2026. 2. 24 (Tue) 16:00-17:00  Room 8309
Kenta Nakamura (Nihon University)

Volume concentration phenomenon for the p-Sobolev flow

ABSTRACT. We provide a new quantitative local boundedness for the p-Sobolev flow, which is a nonlinear generalization of the gradient flow concerning the p-Dirichlet energy on a bounded domain. In the case p=2, the p-Sobolev flow is the heat flow. This estimate enables us to observe a volume concentration phenomenon for the p-Sobolev flow. This is based on a joint work with Tuomo Kuusi and Masashi Misawa.

2026. 3. 23 (Mon) 14:00-15:00  Room 1423
Geuntaek Seo (POSTECH)

TBA

ABSTRACT. TBA

2026. 3. 23 (Mon) 15:00-16:00  Room 1424
Sungjin Lee (Sogang University)

TBA

ABSTRACT. TBA

2026. 3. 23 (Mon) 16:00-17:00  Room 1424
Dong-ha Kim (Ajou University)

TBA

ABSTRACT. TBA

2026. 3. 30 (Mon) 16:00-17:00  Room 1424
Jaeyong Shin (Yonsei University)

TBA

ABSTRACT. TBA

Past Seminars

2026 Seminars
2025 Seminars
2024 Seminars
2023 Seminars
2022 Seminars
2021 Seminars
2020 Seminars
2019 Seminars

Organizers

Jae-Hwan Choi   -   Korea Institute for Advanced Study

Yong-Gwan Ji   -   Korea Institute for Advanced Study

Nam-Gyu Kang   -   Korea Institute for Advanced Study

Taegyu Kim   -   Korea Institute for Advanced Study

Wontae Kim   -   Korea Institute for Advanced Study

Joonhyun La   -   Korea Institute for Advanced Study

Jung-Kyoung Lee   -   Korea Institute for Advanced Study

Juyoung Lee   -   Korea Institute for Advanced Study

Se-Chan Lee   -   Korea Institute for Advanced Study

Sewook Oh   -   Korea Institute for Advanced Study

Sung-Jin Oh   -   UC Berkeley & KIAS

Hyangdong Park   -   Korea Institute for Advanced Study

Junehee Ryu   -   Korea Institute for Advanced Study

Jinsol Seo   -   Korea Institute for Advanced Study

Kyeong Song   -   Korea Institute for Advanced Study

Directions

Korea Institute for Advanced Study
Buildings 1 & 8, 85 Hoegi-ro, Dongdaemun-gu, Seoul, Korea



June E Huh Center for Mathematical Challenges
2nd Floor, 118 Hongneung-ro, Dongdaemun-gu, Seoul, Korea