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]