Microstructural evolution in 3D: an existence result, with David Kinderlehrer, Nonlinear Analysis Vol 258, 113810 (2025)
An explicit formulation of the learned noise predictor $\epsilon_{\theta}({\bf x}_t, t)$ via the forward-process noise $\epsilon_{t}$ in denoising diffusion probabilistic models (DDPMs), arxiv:2507.04203 (2025)
Quantitative estimates for enhancement of the field excited by an emitter due to presence of two closely located spherical inclusions, with H. Kang, Journal of Differential Equations, vol 269, issue 4, 5, 2977-3002 (2020)
Quantitative estimates of the field excited by an emitter in a narrow region between two circular inclusions, with H. Kang, Quart. Appl. Math. 77, 861-873 (2019)
Precise estimates of the field excited by an emitter in presence of closely located inclusions of a bow-tie shape, with H. Kang, Journal of Mathematical Analysis and Applications, Volume 479, Issue 2, 15 (2019)
Optimal estimates of the field enhancement in presence of a bow-tie structure of perfectly conducting inclusions in two dimensions, with H. Kang, Journal of Differential Equations, Volume 266, Issue 8, 5064-5094 (2019)
Two types of electric field enhancements by infinitely many circular conductors arranged closely in two parallel lines, Quarterly of Applied Mathematics (2017)
An optimal estimate for electric fields on the shortest line segment between two spherical insulators in three dimensions, Journal of Differential Equations (2016)
Stability for the Electromagnetic Scattering from Large Cavities, with G. Bao, Archive for Rational Mechanics and Analysis (2015)
Optimal estimates and asymptotic for the stress concentration between closely located stiff inclusions, with H, Kang, H. Lee, Math. Ann. (2015)
Characterization of the electric field concentration between two adjacent spherical perfect conductors, with H. Kang, M. Lim, K., SIAM J. Appl. Math. 74(1)125-146 (2013)
Spectral analysis of the Neumann-Poincaré operator and characterization of the stress concentration in anti-plane elasticity, with H. Ammari, G. Ciraolo, H. Kang, H. Lee, Archive for Rational Mechanics and Analysis (2012), arxiv:1206.207
Asymptotics and computation of the solution to the conductivity equation in the presence of adjacent inclusions with extreme conductivities, with H. Kang, M. Lim, Journal de Mathématiques Pures et Appliquées (2012)
Stability of the scattering from a large electromagnetic cavity in two dimensions, with Gang Bao, Zhengfung Zho, SIAM Journal on Mathematical Analysis 44, no. 1, 383-404 (2012)
Strong influence of a small fiber on shear stress in fiber-reinforced composites, with M. Lim, Journal of Differential Equations 250, no. 5, 2405-2439 (2011)
Blow-up of electric field between closely spaced spherical perfect conductors, with M. Lim, Communications in Partial Differential Equations 34, no. 10-12, 1287-1315 (2009)
Optimal bound on high stresses occurring between stiff fibers with arbitrary shaped cross-sections, Journal of Mathematical Analysis and Applications350, pp. 306-312 (2009)
On the stability of an inverse problem for the wave equation, with Gang Bao, Inverse problems 25, no. 4, 045003, 7 pp (2009)
Estimates for electric fields blown up between closely adjacent conductors with arbitrary shape, SIAM Journal on Applied Mathematics 67, no 3, pp. 714-730 (2007)
Boundary determination of conductivities and Riemannian metrics via local Dirichlet-to-Neumann operator, with H. Kang, SIAM Journal on Mathematical Analysis 34, no.3, 719-735 (2002)
The reflection of solutions of Helmholtz equation and an application, Communications in Korean Mathematical Society 16, no. 3, 427-427 (2001)
Recovery of an inhomogeneity in an elliptic equation, with H. Kang, K. Kwon, Inverse Problems 17, no.1, 25-44 (2001)