Sunhi Choi
Associate Professor
Department of Mathematics
The University of Arizona
617 N Santa Rita Ave, Rm 208
Tucson, Arizona 85721-0089
schoi at math.arizona.edu


RESEARCH ON PARTIAL DIFFERENTIAL EQUATIONS:
My recent research interest is on problems in nonlinear differential equations in which the boundary (zero level set) is unknown and has to be determined. This is so-called free boundary problems. The particular problems that I have worked on include the Stefan problem, Hele-Shaw problem and the flame propagation for laminar flames. The Stefan problem models the phase transition between solid and fluid states such as the interface between water and melting ice. The Hele-Shaw problem models the fluid motion in a narrow cell between two parallel plates. The goal of my research is to gain the regularity properties and study the asymptotic behavior of the free boundaries. I am also interested in 1. the first eigenfunction and eigenvalue for the Laplacian under the Neumann or Dirichlet boundary conditions and 2. periodic homogenization problems for second-order nonlinear pde with oscillatory boundary conditions.


COURSES TAUGHT AT UA:
MATH 124
MATH 125
MATH 129
MATH 215
MATH 323
MATH 355
MATH 527A
MATH 527B


GRANT:
  • NSF, "Partial differential equations and harmonic analysis," PI.



  • PUBLICATIONS:
  • S. Choi, I. Kim, "Homogenization of oblique boundary value problems," arXiv:1911.06909 pdf
  • R. Abrams, S. Choi, "Regularity and asymptotic behavior of laminar flames in higher dimensions," arXiv:1911.06916 pdf
  • S. Choi, I.C. Kim, "Homogenization for nonlinear PDEs in general domains with oscillatory Neumann boundary data," J. Math. Pures Appl. Vol. 102 (2014), no. 2, 419448. doi
  • S. Choi, I.C. Kim, "Homogenization with oscillatory Neumann boundary data in general domain," Geometric partial differential equations, 105118, CRM Series, 15, Ed. Norm., Pisa, 2013. pdf
  • S. Choi, I.C. Kim, K.-A. Lee, "Homogenization of Neumann boundary data with fully nonlinear operator," Analysis & PDE Vol. 6 (2013), No. 4, 951-972. doi
  • S. Choi, I. Kim, "The two-phase Stefan problem: regularization near Lipschitz initial data by phase dynamics," Analysis & PDE Vol. 5 (2012), No. 5, 1063-1103. doi
  • S. Choi, I. Kim, "Regularity of one-phase Stefan problem near Lipschitz initial data," Amer. J. Math. 132 (2010), no. 6, 1693-1727. pdf
  • S. Choi, D. Jerison, I. Kim, "Local regularization of the one-phase Hele-Shaw flow," Indiana Univ. Math. J. 58 (2009), no. 6, 2765-2804. pdf
  • S. Choi, "Regularity near a contact point for flame propagation," Comm. Partial Differential Equations 34 (2009), no. 4-6, 457-474. pdf
  • S. Choi, D. Jerison, I. Kim, "Locating the first nodal set in higher dimensions," Trans. Amer. Math. Soc., 361 (2009), no. 10, 5111-5137. pdf
  • S. Choi, D. Jerison, I. Kim, "Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface," Amer. J. Math. 129 (2007), no. 2, 527-582. pdf
  • S. Choi, I. Kim, "Waiting time phenomena for the Hele-Shaw and the Stefan problem," Indiana Univ. Math. J., 55 (2006), no. 2, 525-551. pdf
  • S. Choi, "The lower density theorem for harmonic measure," J. d'Analyse Math., 93 (2004), 237-269. pdf