- 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]