Cristian Rios

Associate Professor; Associate Head Research

Department of Mathematics and Statistics

PhD

University of Minnesota, 2001

MMath

University of Minnesota, 1998

Contact information

Phone

Office: 403.220.3221

Web presence

website

Location

Office : MS546

Courses


Research and teaching

Research areas

  • Analysis and partial differential equations
  • Quasilinear and fully nonlinear partial differential equations
  • Degenerate elliptic equations
  • Monge-Ampere equations
  • Evolutionary equations

Publications

Journal articles - peer reviewed

  • Rios, Cristian, David Cruz-Uribe and José María Martell. "On the Kato problem and extensions for degenerate elliptic operators.". Analysis and PDE 11.3 (2018): 609-660. Print.
  • Rios, Cristian, Lyudmila Korobenko and Diego Maldonado. "From Sobolev Inequality to Doubling". Proceedings of the American Mathematical Society 143.9 (2015): 4017-4028. Print.
  • Rios, Cristian and Cruz-Uribe, David. "The Kato problem for operators with weighted ellipticity". Transactions of the American Mathematical Society 367.7 (2015): 4727-4756. Print.
  • Rios, Cristian and Korobenko, Lyudmila. "Hypoellipticity of certain infinitely degenerate second order operators". Journal of Mathematical Analysis and Applications 409.1 (2014): 41–55. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "Hypoellipticity for infinitely degenerate quasilinear equations and the Dirichlet problem". Journal d'Analise Mathematíque 119. (2013): 1-62. Print.
  • Rios, Cristian and Cruz-Uribe, David. "The solution of the Kato problem for degenerate elliptic operators with Gaussian bounds". Transactions of the American Mathematical Society 364.7 (2012): 3449–3478. Print.
  • Rios, Cristian and Sawyer, Eric. "Smoothness of radial solutions to Monge-Ampère equations". Proceedings of the American Mathematical Society 137.4 (2009): 1373-1379. Print.
  • Rios, Cristian and Cruz-Uribe, David. "Gaussian bounds for degenerate parabolic equations". Journal of Functional Analysis 255.8 (2008): 283-312. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "Regularity of subelliptic Monge-Ampère equations". Advances in Mathematics 217.3 (2008): 967-1026. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "A priori estimates for infinitely degenerate quasilinear equations". Differential Integral Equations 21.1-2 (2008): 131-200. Print.
  • Rios, Cristian. "L^p regularity of the Dirichlet problem for elliptic equations with singular drift". Publicacions Mathematíque 50.2 (2006): 475-507. Print.
  • Rios, Cristian, Sawyer, Eric and Wheeden, Richard. "A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations". Advances in Mathematics 193.2 (2005): 373-415. Print.
  • Rios, Cristian. "The L^p Dirichlet problem and nondivergence harmonic measure". Transactions of the American Mathematical Society 355.2 (2003): 665-687. Print.

PhD thesis

  • Rios, Cristian. Sufficient conditions for the absolute continuity of the nondivergence harmonic measure 2001.