University of Kentucky College of Arts & Sciences

Research Groups

Analysis and Partial Differential Equations

Faculty

David R. Adams

Professor (Potential Theory and Partial Differntial Equations), Ph.D, Univ.of Minnesota, 1969
James E. Brennan Professor (Potential Theory and Complex Analysis) Ph.D, Brown Univ, 1968
Russell Brown Professor (Harmonic Analysis and Partial Differential Equations), Ph.D, Univ of Minnesota, 1987
Richard Carey Professor (Functional Analysis), Ph.D, SUNY-Stony Brook, 1970
Peter Hislop Professor (Mathematical Physics), Ph D, Univ of California-Berkeley, 1984
John L. Lewis Professor (Mathematical Aspects of Material Differential Equations), Ph D, Univ of Illinois-Urbana Champaign, 1970
Katharine Ott NSF Postdoctoral Fellow (Harmonic Analysis and Partial Differential Equations), Ph D., Univ. of Virgina, 2008
Peter Perry Professor (Mathematical Physics), Ph D, Princeton Univ, 1981
Zhongwei Shen Professor and Chair (Partial Differntial Equations, Harmonic Analysis, and Mathematical Physics), Ph D, Univ. of Chicago, 1989.
Ted Suffridge Professor (Complex Analysis), PhD, Univ of Kansas, 1965
Changyou  Wang Professor (Nonlinear Partial Differential Equations), PhD. Rice Univ, 1996.

Emeritus Faculty

J.D. Buckholtz

Complex Analysis
Michael Freeman Several Complex Variables
Ronald F. Gariepy Partial Differential Equations
Henry Howard Qualitative Theory of Ordinary Differential Equations
Ray Rishel Stochastic Optimal Control Theory

Current Ph.D Students
Jun Geng
Phuoc Ho
Tao Huang
Nicholas Kirby
Julie Miker
Erin Militzer
Zhongyi Nie
Justin Taylor
Ryan Walker

Ph.D. Dissertations Since 1989

  • Joel Kilty (2009), L^p Boundary Value Problems on Lipschitz Domains (Advisor: Z. Shen).
  • Teng Jiang (2008), Absolute Minimizers of L-infinity Functional under the Dirichlet Energy Constraint (Advisor: C. Wang).
  • Christopher Frayer (2008), Scattering Theory on the Line with Singular Miura Potentials (Advisor: P. Perry).
  • Aekyoung Shin Kim (2007), The L^p Neumann Problem for Laplace Equation in Convex Domains (Advisor: Z. Shen).
  • Yuho Shin (2006), Geodesics of a Two-Step Nilpotent Lie Group (Advisor: P. Perry).
  • Bjorn Bennewitz (2006), Nonuniqueness in a Free Boundary Problem (Advisor: J. L. Lewis).
  • Mike Dobranski (2004), Construction of Exponentially Growing Solutions to First-Order Systems with Non-Local Potentials (Adviosr: R. Brown).
  • Mary Goodloe (2004), Hadamard Products of Convex Harmonic Mappings (Advisor: T. Suffridge).
  • Stacey Mueller (2004), Harmonic Mappings and Solutions of a Differential Equation Related to de la Vallee Poussin Means (Advisor: T. Suffridge).
  • Wataru Ishizuka (2003), The Weak Compactness and Regularity of Weakly Harmonic Maps (Advisors: C. Wang and L. Harris).
  • Christopher Morgan (2001), On Univalent Harmonic Mappings (Advisor: T. Suffridge).
  • Jeffery D. Sykes (1999), Regularity of Solutions of the Mixed Boundary Problem for Laplace's Equation on a Lipschitz Graph Domain (Advisor: R. Brown).
  • Jerry R. Muir, Jr. (1999), Linear and Holomorphic Idempotents and Retracts in the Open Unit Ball of a Commutative C*-algebra with Identity (Advisor: T. Suffridge ).
  • Michael D. Galloy (1998), Harmonic Univalent Mappings on the Unit Disk and the Punctured Unit Disk (Advisor: T. Suffridge ).
  • John T. Thompson (1998), A Study of Harmonic Mappings on Punctured Domains: An Argument Principle and Some Coefficient Results (Advisor: T. Suffridge).
  • Wei Hu (1997), The Initial-boundary Value Problem for Higher Order Differential Operators on Lipschitz Cylinders (Advisor: R. Brown).
  • John Prather (1997), Geometric Properties of the Hadamard Product (Advisor: T. Suffridge).
  • Michael Dorff (1997), The Inner Mapping Radius and Construction of Harmonic, Univalent Mappings of the Unit Disk (Advisor: T. Suffridge).
  • John Tolle (1996), Location of Inhomogeneities in Elastic Media (Advisor: R. Gariepy).
  • Ron Vandenhouten (1996), Stability for the Biharmonic and Polyharmonic Obstacle Problems (Advisor: D. R. Adams).
  • Kevin Roper (1995), Convexity Properties of Holomorphic Mappings in C (Advisor: T. Suffridge).
  • Evelyn Pupplo-Cody (1992), A Structural Formula for a Class of Typically Real Functions and Some Consequences (Advisor: T. Suffridge).
  • Barbara Hatfield (1991), Gradient Estimates for Capillary Problems (Advisor: R. Gariepy).
  • Hi Jun Choe (1989), Regularity for Minimizers of Certain Singular Functionals (Advisor: R. Gariepy).

Partial Differential Equations Seminar

Tuesdays at 11:00 A.M.; Coordinator: Katie Ott .


 
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