### Preprints

Extremals in nonlinear potential theory, with Francis Seuffert. arxiv.org/abs/2005.13615.

On the symmetry and monotonicity of Morrey extremals, with Francis Seuffert. arxiv.org/abs/1912.11574.

Asymptotic flatness of Morrey extremals, with Francis Seuffert. arxiv.org/abs/1905.07060.

A trajectory map for the pressureless Euler equations. arxiv.org/abs/1902.04197.

Newton’s second law with a semiconvex potential. arxiv.org/abs/1812.07089.

Extremal functions for Morrey’s inequality, with Francis Seuffert. arxiv.org/abs/1810.04393.

Sticky particles and the pressureless Euler equations in one spatial dimension. arxiv.org/abs/1804.09340.

Probability measures on the path space and the sticky particle system. arxiv.org/abs/1804.09343.

Large time behavior of solutions of Trudinger’s equation, with Erik Lindgren. arxiv.org/abs/1702.01630.

### Publications

Lagrangian coordinates for the sticky particle system. SIAM J. Math. Anal. Vol. 51 (2019), No. 5, pp. 3769–3795

Lipschitz Regularity for a Homogeneous Doubly Nonlinear PDE, with Erik Lindgren. SIAM J. Math. Anal. Vol. 51 (2019), No. 4, pp. 3606–3624

Partial Regularity for Doubly Nonlinear Parabolic Systems of the First Type. Indiana Mathematics Journal Vol. 68, No. 2 (2019).

Sticky Particle Dynamics on the Real Line, Notices of the American Mathematical Society 66 (2019), no. 2, 162-168.

Extremal functions for Morrey’s inequality in convex domains, with Erik Lindgren, Mathematische annalen (2018).

Partial regularity for type two doubly nonlinear parabolic systems, Archive for Rational Mechanics and Analysis (2018), no.1, 591-636.

Approximation of the least Rayleigh quotient for degree p homogeneous functionals, with Erik Lindgren, Journal of Functional Analysis 272 (2017) 4873–4918.

An eigenvalue problem for fully nonlinear elliptic equations with gradient constraints, Calculus of Variations and Partial Differential Equations 56 (2017), no. 2, 56:34.

Compactness methods for doubly nonlinear parabolic systems, Transactions of the American Mathematical Society 369 (2017), no. 7, 5031–5068.

Plateau’s Rotating drops and rotational figures of equilibrium, with Jeffrey Elms, Roberto Lopez, and John McCuan, J. Math. Anal. Appl. 446 (2017) 201–232.

Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution, with Erik Lindgren, Analysis & PDE 9 (2016), no. 6, 1447–1482.

A doubly nonlinear evolution for the optimal Poincaré inequality, with Erik Lindgren, Calc. Var. Partial Differential Equations 55 (2016), no. 4, Paper No. 100, 22 pp.

On Hamilton-Jacobi-Bellman equations with convex gradient constraints, with Henok Mawi, Interfaces and Free Boundaries 18 (2016), 291–315.

Inverse iteration for p-ground states, with Erik Lindgren, Proceedings of the American Mathematical Society 144 (2016), 2121–2131.

Value functions in the Wasserstein spaces: finite time horizons, with Hwa Kil Kim, Journal of Functional Analysis 269 (2015) 968–997.

Infinite horizon value functions in the Wasserstein spaces, with Hwa Kil Kim, Journal of Differential Equations 258 (2015) 1933–1966.

Option pricing in the large risk aversion, small transaction cost limit, Communications in Partial Differential Equations, Volume 39 Issue 11 (2014) 1998-2027.

Partial regularity of weak solutions of the viscoelastic Navier-Stokes equations with damping, SIAM J. Math. Anal. 45 (2013), no. 2, 495–517.

Nonuniqueness of infinity ground states, with Charles Smart and Yifeng Yu, Calculus of Variations and Partial Differential Equations, (2013) Volume 48, Issue 3–4, pp 545–554.

A blowup criterion for ideal viscoelastic flow, with Xianpeng Hu, by Journal of Mathematical Fluid Mechanics, (2013), Volume 15, Issue 3, pp 431–437.

Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control, ESAIM Control Optim. Calc. Var. 19 (2013), no. 1, 112–128.

The eigenvalue problem of singular ergodic control, Communications of Pure and Applied Mathematics 65 (2012), no. 5, 649–682.

Symmetric constant mean curvature surfaces in S3, with Sung Ho Park and John McCuan, Pacific Journal of Mathematics Volume 241 (2009), no. 1, 63-115.

Toroidal Rotating Drops, with John McCuan, Pacific Journal of Mathematics Volume 224 (2006), no. 2, 279-289.

### Current Funding

National Science Foundation CAREER (DMS-1554130)

### Past Funding

National Science Foundation mathematical sciences grant (DMS-1301628)

Simons Foundation Collaboration Grants for Mathematicians (MPS-283346)

National Science Foundation postdoctoral research fellowship (DMS-1004733)

National Science Foundation graduate research fellowship

Lucent Technologies/Bell Labs graduate research fellowship