Analysis and Partial Differential Equations
Faculty | |
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James Brennan | Professor (Potential Theory and Complex Analysis), Ph.D., Brown University, 1968 |
Russell Brown | Professor (Harmonic Analysis, Inverse Problems, PDE), Ph.D., University of Minnesota, 1987 |
Richard Carey | Professor (Functional Analysis), Ph.D., SUNY-Stony Brook, 1970 |
Francis Chung | Assistant Professor (Inverse Problems, Mathematical Physics, Partial Differential Equations, Harmonic Analysis), Ph.D., University of Chicago, 2012 |
Lawrence Harris | Professor (Functional analysis, Infinite-Dimensional Holomorphy, Polynomials), Ph.D., Cornell University, 1969 |
Peter Hislop | Professor (Mathematical Physics and Geometric Analysis), Ph.D., University of California-Berkeley, 1984 |
Peter Perry | Professor (Mathematical Physics, Geometric Analysis, Dispersive Nonlinear PDE), Ph.D., Princeton University, 1981 |
Zhongwei Shen | Professor (Partial Differential Equations, Harmonic Analysis, and Mathematical Physics), Ph.D., University of Chicago, 1989 |
Mihai Tohaneanu | Assistant Professor (Analysis and Partial Differential Equations), Ph.D., University of California-Berkeley, 2012 |
Partial Differential Equations
Emeritus Faculty | |
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David Adams | Potential Theory and Partial Differential Equations |
J.D. Buckholz | Complex Analysis |
Ray Cox | Analysis |
Ronald Gariepy | Partial Differential Equations |
Henry Howard | Qualitative Theory of Ordinary Differential Equations |
John Lewis | Partial Differential Equations |
Ray Rishel | Stochastic Optimal Control Theory |
Ted Suffridge | Complex Analysis |
James Wells | Analysis, Numerical Analysis |
Current Ph.D Students |
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Maryam Al Ghafli (Hislop) |
Benjamin Brodie (Hislop) |
Samuel Herschenfeld (Hislop) |
Joel Klipfel (Perry) |
Shi-Zhuo Looi (Tohaneanu) |
George Lytle (Perry) |
Jinping Zhuge (Shen) |
Analysis and Partial Differential Equations Seminar
Tuesdays at 11:00 A.M.; Coordinator: Mihai Tohaneanu Seminar schedule
Ohio River Analysis Meeting
The Ohio River Analysis Meeting is a joint effort between the University of Kentucky and the University of Cincinnati. The ninth meeting will be held in Cincinnati on March 30-31, 2019.
The Van Winter Lecture
The Department hosted Gigliola Staffilani, who gave the Van Winter Lecture in Mathematical Physics on Monday, 4 November 2018.
Ph.D. Dissertations Since 1989
- Stephen Deterding (2018), Bounded Point Derivations on Certain Function Spaces (advisor: J. Brennan)
- B. Chase Russell (2018), Homogenization in Perforated Domains and with Soft Inclsuions (advisor: Z. Shen)
- Joseph Lindgren (2017), Orbital Stability of Solitons Solving Non-Linear Schrödinger Equations in an External Potential (advisor: P. Hislop)
- Jiaqi Liu (2017), Global Well-Posedness for the Derivative Nonlinear Schrödinger Equation Through Inverse Scattering (advisor: P. Perry)
- Morgan Schreffler (2017), Approximation of Solutions to the Mixed Dirichlet-Neumann Boundary Value Problem on Lipschitz Domains (advisor: R. Brown)
- Robert Wolf (2017), Compactness of Isoresonant Potentials (advisor: P. Hislop)
- Laura Croyle (2016), Solutions to the Lp Mixed Boundary Value Problem in C^{1,1} Domains (Advisor: R. Brown)
- Shu Gu (2016), Homogenization of Stokes Systems with Periodic Coefficients (Advisor: Z. Shen)
- Michael Music (2016), Inverse Scattering for the Zero-Energy Novikov-Veselov Equation (Advisor: P. Perry)
- Yaowei Zhang (2016), The Bourgain Spaces and Recovery of Magnetic and Electric Potentials of Schr\”{o}dinger Operators (Advisor: R. Brown)
- Aaron Saxton (2014), Decay estimates on trace norms of locaized functions of Schrödinger operators (Advisor: P. Hislop)
- Murat Akman (2014), On The Dimension of a Certain Measure Arising From a Quasilinear Elliptic PDE (Advisor: J. Lewis)
- Megan Gier (2014), Eigenvalue Multiplicities of the Hodge Laplacian on Coexact 2-forms for Generic Metrics on 5-Manifolds (Advisor: P. Hislop)
- Tao Huang (2013), Regularity and Uniqueness of Harmonic and Biharmonic Map Heat Flows (Advisor: C. Wang).
- Ryan Walker (2013), On a Paley-Wiener Theorem for the ZS-AKNS Scattering Transform (Advisor: P. Perry).
- Jay Hineman (2012), The Hydrodynamic Flow of Nematic Liquid Crystals in Three Dimensions (Advisor: C. Wang
- Chris Mattingly (2012), Rational Approximation on Compact Nowhere Dense Sets (Advisor: J. Brennan).
- Jun Geng (2011), Elliptic Boundary Value Problems on Non-smooth Domains (Advisor: Z. Shen).
- Erin Militzer (2011), L^{p} Polynomial Approximation and Uniform Rational Approximation (Advisor: J. Brennan).
- Justin Taylor (2011), Convergence of Eigenvalues for Elliptic Systems on Domains with Thin Tubes and the Green Function for the Mixed Problem (Advisor: R. Brown).
- Phuoc Ho (2010), Upper Bounds on the Splitting of Eigenvalues (Advisor: P. Hislop).
- Joel Kilty (2009), L^{p} Boundary Value Problems on Lipschitz Domains (Advisor: Z. Shen).
- Julie Miker (2009), Eigenvalue Inequalities for a Family of Spherically Symmetric Riemannian Manifolds (Advisor: P. Hislop).
- Zhongyi Nie (2009), Estimates for a Class of Multi-linear forms (Advisor: R. Brown).
- Teng Jiang (2008), Absolute Minimizers of L^{∞} 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 (Advisor: R. Brown).
- Mary Goodloe (2004), Hadamard Products of Convex Harmonic Mappings (Advisor: T. Suffridge).
- Steve Kovacs (2004), Invertibility Preserving maps of C^{*}-Algebras (Advisor: L. Harris).
- 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).
- Carl Lutzer (2000), On the extraction of topological and geometric information from the spectrum of the Dirichlet to Neumann operator (Advisor: P. Hislop).
- 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).
- Robert Robertson (1996), An inverse boundary value problem in linear elasticity (Advisor: P. Hislop).
- 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).