Faculty Profiles

Guillen, N., Edelstein, M., Ben-Chen, M., & Solomon, J. (2023). A Convex Optimization Framework for Regularized Geodesic Distances. https://doi.org/10.48550/arXiv.2305.13101

Guillen, N., & Gualdani, M. P. (2022). Hardy’s inequality and the isotropic Landau equation. Journal of Functional Analysis, 283(6). https://doi.org/10.1016/j.jfa.2022.109559

Guillen, N., Kim, I., & Mellet, A. (2022). A Hele-Shaw limit without monotonicity. Archive for Rational Mechanics and Analysis. https://doi.org/10.1007/s00205-021-01750-4

Guillen, N., & Kitagawa, J. (2020). Optimal transport and the Gauss curvature equation. Methods and Applications of Analysis, 27(Special Issue for the 60th Birthday of John Urbas), 387–404. https://doi.org/https://dx.doi.org/10.4310/MAA.2020.v27.n4.a5

Guillen, N., Kitagawa, J., & Schwab, R. W. (2020). Estimates for Dirichlet-to-Neumann Maps as Integro-differential Operators. Potential Analysis, 53(2), 483–521. https://doi.org/10.1007/s11118-019-09776-w

Guillen, N., & Schwab, R. W. (2020). Min–Max formulas for nonlocal elliptic operators on Euclidean Space. Nonlinear Analysis, 193, 111468. https://doi.org/10.1016/j.na.2019.02.021

Abrishami, T., Guillen, N., Rule, P., Schutzman, Z., Solomon, J., Weighill, T., & Wu, S. (2020). Geometry of graph partitions via optimal transport. SIAM Journal on Scientific Computing, 42(5), A3340–A3366. https://doi.org/10.1137/19M1295258

Guillen, N., & Schwab, R. W. (2019). Min–max formulas for nonlocal elliptic operators. Calculus of Variations and Partial Differential Equations, 58(6). https://doi.org/10.1007/s00526-019-1631-z

Guillen Matheus, N. D., & Gualdani, M. (2019). On $A_p$ weights and the Landau equation. Calculus of Variations and Partial Differential Equations. https://doi.org/10.1007/s00526-018-1451-6

Chang-Lara, H. A., Guillen, N., & Schwab, R. W. (2019). Some free boundary problems recast as nonlocal parabolic equations. Nonlinear Analysis, 189, 111538. https://doi.org/10.1016/j.na.2019.05.019

Guillen, N. (2019). A primer on generated jacobian equations: Geometry, optics, economics. Notices of the American Mathematical Society, 66(9), 1401–1411. https://doi.org/10.1090/noti1956

Guillen, N., Mou, C., & Świȩch, A. (2019). Coupling Lévy measures and comparison principles for viscosity solutions. Transactions of the American Mathematical Society, 372(10), 7327–7370. https://doi.org/10.1090/tran/7877

Guillen, N., & Schwab, R. W. (2018). Neumann Homogenization via Integro-Differential Operators. Part 2: Singular Gradient Dependence. SIAM Journal on Mathematical Analysis, 50(2), 1679–1719. https://doi.org/10.1137/16m1080860

Guillen, N., & Kitagawa, J. (2017). Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations. Communications on Pure and Applied Mathematics, 70(6), 1146–1220. https://doi.org/10.1002/cpa.21691

Guillen, N., & Schwab, R. W. (2016). Neumann homogenization via integro-differential operators. Discrete and Continuous Dynamical Systems, 36(7), 3677–3703. https://doi.org/10.3934/dcds.2016.36.3677

Gualdani, M. P., & Guillen, N. (2016). Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential. Analysis and PDE, 9(8), 1773–1810. https://doi.org/10.2140/apde.2016.9.1773

Guillen, N., & Kitagawa, J. (2015). On the local geometry of maps with c-convex potentials. Calculus of Variations and Partial Differential Equations, 52(1–2), 345–387. https://doi.org/10.1007/s00526-014-0715-z

Guillen, N., & Kim, I. (2015). Quasistatic Droplets in Randomly Perforated Domains. Archive for Rational Mechanics and Analysis, 215(1), 211–281. https://doi.org/10.1007/s00205-014-0777-2

van Gennip, Y., Guillen, N., Osting, B., & Bertozzi, A. L. (2014). Mean Curvature, Threshold Dynamics, and Phase Field Theory on Finite Graphs. Milan Journal of Mathematics, 82(1), 3–65. https://doi.org/10.1007/s00032-014-0216-8

Guillen, N., & Schwab, R. W. (2012). Aleksandrov–Bakelman–Pucci Type Estimates for Integro-Differential Equations. Archive for Rational Mechanics and Analysis, 206(1), 111–157. https://doi.org/10.1007/s00205-012-0529-0

Guillen, N. (2009). Optimal regularity for the Signorini problem. Calculus of Variations and Partial Differential Equations, 36(4), 533–546. https://doi.org/10.1007/s00526-009-0242-5