Sunhi Choi
Assistant Professor
Department of Mathematics
The University of Arizona
617 N Santa Rita Ave, Rm 610
Tucson, Arizona 85721-0089
schoi at math.arizona.edu

My CV

RESEARCH ON PARTIAL DIFFERENTIAL EQUATIONS AND COMPLEX ANALYSIS:
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 problem. The particular problems that I have worked on include the Stefan problem and the Hele-Shaw problem. 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 the asymptotic behavior of the free boundary.

Another focus of my research is to study the first eigenfunction and eigenvalue for the Laplacian under the Neumann or Dirichlet boundary conditions. The physical model of the Neumann problem is a vibrating membrane with free ends. The first eigenfunction is the lowest mode of vibration, and the frequency of vibration is the first eigenvalue. I am interested in describing the shape of level sets and estimating the eigenvalues.

COURSES TAUGHT AT UA:
MATH 124 (Fall 2006)
MATH 129 (Spring 2007)
MATH 215 (Fall 2007)
MATH 323 (Spring 2008)

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


    • PUBLICATIONS:
  • S. Choi, I. Kim, "Regularity of one-phase Stefan problem," preprint.
  • S. Choi, D. Jerison, I. Kim, "A local regularization theorem on one-phase Hele-Shaw," preprint.
  • S. Choi, D. Jerison, I. Kim, "Locating the first nodal set in higher dimensions," Trans. Amer. Math. Soc., to appear.
  • S. Choi, D. Jerison, I. Kim, "Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface," Amer. J. Math. vol. 129, no. 2, pp. 527-582 (2007).
  • S. Choi, I. Kim, "Waiting time phenomena for the Hele-Shaw and the Stefan problem," Indiana Univ. Math. J., vol. 55, pp. 525-552 (2006).
  • S. Choi, "The lower density theorem for harmonic measure," J. d'Analyse Math., vol. 93, pp. 237-270 (2004).

    • Last updated: 1/28/2008