Qingbo Huang, Ph.D.

Mathematics & Statistics
Professor Mathematics and Statistics
Math/Microbiology Bldg 245, 3640 Colonel Glenn Hwy., Dayton, OH 45435-0001


Research statement: 
  • My Research Interests:  nonlinear PDEs, geometric optics, and real harmonic analysis.

Preprints & Recent Papers:

  • Q. Huang, M.-Y. Lee & C.-C. Lin, The John-Stromberg inequality and functions in VMO type spaces over families of sets and applications to the Monge-Ampere equation, 31 pages, preprint.
  • Q. Huang, Regularity theory for Ln-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity, 34 pages, to appear in Ann. Inst. H. Poincare Anal. Non Lineaire.
  • C. Gutierrez, Q. Huang & H. Mawi, Refractors in anisotropic media associated with norms, Nonlinear Analysis 188 (2019), 125-141. 

More Publications: 

  • C. Gutierrez & Q. Huang,  The near field refractor,  Ann. Inst. H. Poincare Anal. Non Lineaire  31(2014), 655-684.   
  • Q. Huang,  Sharp regularity results on second derivatives of solutions to the Monge-Ampere equation with VMO type data,  Comm. Pure Appl. Math.  62 (2009), 677-705. 
  • L. A. Caffarelli & Q. Huang,  Reflector problem in R^n endowed with non-Euclidean norm, Arch. Rational Mech. Anal, 193 (2009), 445-473. 
  • C. Gutierrez & Q. Huang,  The refractor problem in reshaping light beams,  Arch. Rational Mech. Anal, 193 (2009), 423-443. 
  • L. A. Caffarelli,  C. Gutierrez & Q. Huang,  On the Regularity of  Reflector Antennas,  Annals of Math.  167 (2008), 299-323. 
  • Q. Huang,  On the mean oscillation of the Hessian of solutions to the Monge-Ampere equation,  Advances in Math.  207 (2006), 599-616.
  • Q. Huang & G. Lu,  On a priori C^{1,alpha} and  W^{2,p} estimates for a parabolic Monge-Ampere equation in the Gauss curvature flows,  Amer. J. Math. 128 (2006),  453-480.  
  • L. A. Caffarelli & Q. Huang,  Estimates in the Generalized Campanato-John-Nirenberg Spaces for Fully Nonlinear Elliptic Equations, Duke Math. J.  118 (2003), 1-17.
  • Q. Huang, On the Regularity of Solutions to Fully Nonlinear Elliptic Equations via Liouville Property , Proc. AMS 130 (2002), 1955-1959.
  • C. Gutierrez & Q. Huang, W^{2,p} Estimates for the Parabolic Monge-Ampere Equation , Arch. Rational Mech. Anal.  159 (2001), 137-177.
  • C. Gutierrez & Q. Huang, Geometric Properties of the Sections of Solutions to the Monge-Ampere Equation , Trans. Amer. Math. Soc. 352 (2000), 4381-4396.
  • Q. Huang, Harnack Ineqality for the Linearized Parabolic Monge-Ampere Equation , Trans. Amer. Math. Soc. 351 (1999), 2025-2054.
  • C. Gutierrez & Q. Huang, A Generalization of a Theorem by Calabi to the Parabolic Monge-Ampere Equation , Indiana Univ. Math. J. 47 (1998), 1459-1480.
  • Q. Huang, Estimates on the Generalized Morrey Spaces L_\phi^{2,\lambda} and BMO_\psi for Linear Elliptic Systems , Indiana Univ. Math. J. 45 (1996), 397-439. 




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