Nestor Guillen


Associate Professor
Texas State University - Department of Mathematics
Office: MCS 468
Email: nestor@txstate.edu


Publications
Blog • Nonlocal Wiki
  • Hardy's inequality and the isotropic Landau equation
    Joint work with Maria Gualdani.
    Journal of Functional Analysis, accepted for publication. [arXiv]

  • A Hele-Shaw limit without monotonicity.
    Joint work with Inwon Kim and Antoine Mellet.
    Archive for Rational Mechanics and Analysis (2022). [arXiv] [Journal]

  • Optimal transport and the Gauss curvature equation.
    Joint work with Jun Kitagawa.
    Methods and Applications of Analysis (2020). [arXiv] [Journal]

  • Geometry of Graph Partitions via Optimal Transport.
    Joint work with Tara Abrishami, Parker Rule, Zachary Schutzman, Justin Solomon, Thomas Weighill, and Si Wu.
    SIAM Journal on Scientific Computing (2020). [arXiv] [Journal]

  • A primer on Generated Jacobian Equations: Geometry, Optics, Economics.
    Notices of the American Mathematical Society (2019). [Article]

  • Min-max formulas for nonlocal elliptic operators on Euclidean space.
    Joint work with Russell Schwab.
    Journal of Nonlinear Analysis (2019). [arXiv] [Journal]

  • Some free boundary problems recast as nonlocal parabolic equations.
    Joint work with Hector Chang-Lara and Russell Schwab.
    Journal of Nonlinear Analysis (2019). [arXiv] [Journal]

  • Coupling Levy measures and comparison principles for viscosity solutions.
    Joint work with Chenchen Mou and Andrzej Swiech.
    Transactions of the American Mathematical Society (2019). [arXiv] [Journal]

  • Estimates for Dirichlet-to-Neumann maps as integro-differential operators.
    Joint work with Russell Schwab and Jun Kitagawa.
    Potential Analysis (2019). [arXiv] [Journal]

  • On $A_p$ weigths and the Landau equation.
    Joint work with Maria Gualdani.
    Calculus of Variations and Partial Differential Equations (2019). [arXiv]
    [Journal]

  • Min-max formulas for nonlocal elliptic operators.
    Joint work with Russell Schwab.
    Calculus of Variations and Partial Differential Equations (2019). [arXiv] [Journal]

  • From the free boundary condition for Hele-Shaw to a fractional parabolic equation.
    Joint work with Héctor Chang-Lara.
    Preprint. [arXiv]

  • Neumann Homogenization via Integro-Differential Operators, Part 2: singular gradient dependence.
    Joint work with Russell Schwab.
    SIAM Journal on Mathematical Analysis (2018). [arXiv] [Journal]

  • Pointwise estimates and regularity in geometric optics and other Generated Jacobian Equations.
    Joint work with Jun Kitagawa.
    Communications on Pure and Applied Mathematics (2017). [arXiv] [Journal]

  • Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential.
    Joint work with Maria Gualdani.
    Analysis & PDE (2016). [arXiv] [Journal]

  • Neumann Homogenization via Integro-Differential Operators.
    Joint work with Russell Schwab.
    Discrete and Continuous Dynamical Systems (2016). [arXiv] [Journal]

  • Mean curvature, threshold dynamics, and phase field theory on finite graphs.
    Joint work with Andrea Bertozzi, Yves Van Gennip, and Braxton Osting.
    Milan Journal of Mathematics (2014). [arXiv] [Journal]

  • Quasistatic droplets in randomly perforated domains.
    Joint work with Inwon Kim.
    Archive for Rational Mechanics and Analysis (2015). [arXiv] [Journal]

  • On the local geometry of maps with c-convex potentials.
    Joint work with Jun Kitagawa.
    Calculus of Variations and Partial Differential Equations (2012). [arXiv] [Journal]

  • Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations.
    Joint work with Russell Schwab.
    Archive for Rational Mechanics and Analysis (2012). [arXiv] [Journal]

  • Five lectures on optimal transportation: geometry, regularity and applications.
    Joint work with Robert McCann.
    Analysis and Geometry of Metric Measure Spaces: Lecture Notes of the Séminaire de Mathématiques Supérieure (SMS), Montréal (2012). [pdf] [Book]

  • Regularity for non-local almost minimal boundaries and applications.
    Joint work with Cristina Caputo.
    Preprint. [arXiv]

  • Optimal regularity for the Signorini problem.
    Calculus of Variations and Partial Differential Equations (2009). [arXiv] [Journal]