Courses Taught
Number | Name | Level |
|---|---|---|
MATH 1941 | Honors Calculus I | Undergraduate |
MATH 3137 | Real & Complex Analysis I | Undergraduate |
MATH 8041 | Real Analysis I | Graduate |
MATH 8042 | Real Analysis II | Graduate |
MATH 8141 | Partial Differential Equations I | Graduate |
MATH 9400 | Topics in Analysis | Graduate |
Selected Publications
Recent
Gutiérrez, C. & Pallucchini, L. (2018). Reflection and refraction problems for metasurfaces related to Monge–Ampère equations. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 35(9), 1523-1531. doi: 10.1364/JOSAA.35.001523.
Gutiérrez, C. & Sabra, A. (2018). Freeform Lens Design for Scattering Data with General Radiant Fields. Archive for Rational Mechanics and Analysis, 228(2), 341-399. doi: 10.1007/s00205-017-1196-y.
Biswas, S., Gutiérrez, C., Nemilentsau, A., Lee, I., Oh, S., Avouris, P., & Low, T. (2018). Tunable Graphene Metasurface Reflectarray for Cloaking, Illusion, and Focusing. Physical Review Applied, 9(3). doi: 10.1103/PhysRevApplied.9.034021.
Abedin, F., Gutiérrez, C., & Tralli, G. (2017). Harnack’s inequality for a class of non-divergent equations in the Heisenberg group. Communications in Partial Differential Equations, 42(10), 1644-1658. doi: 10.1080/03605302.2017.1384836.
Abedin, F. & Gutiérrez, C. (2017). An iterative method for generated Jacobian equations. Calculus of Variations and Partial Differential Equations, 56(4). doi: 10.1007/s00526-017-1200-2.
Gutiérrez, C., Pallucchini, L., & Stachura, E. (2017). General refraction problems with phase discontinuities on nonflat metasurfaces. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 34(7), 1160-1172. doi: 10.1364/JOSAA.34.001160.
Leo, R.D., Gutiérrez, C., & Mawi, H. (2017). On the numerical solution of the far field refractor problem. Nonlinear Analysis, Theory, Methods and Applications, 157, 123-145. doi: 10.1016/j.na.2017.03.009.
Gutiérrez, C. (2017). Form-Invariance of Maxwell equations in integral form. doi: 10.1007/978-3-319-52742-0_5.
Gutiérrez, C. & Stachura, E. (2016). Metamaterial lens design. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 33(10), 2020-2026. doi: 10.1364/JOSAA.33.002020.
Abedin, F., Gutiérrez, C., & Tralli, G. (2016). C1,αestimates for the parallel refractor. Nonlinear Analysis, Theory, Methods and Applications, 142, 1-25. doi: 10.1016/j.na.2016.04.001.
Gutiérrez, C. & Sabra, A. (2016). Aspherical lens design and imaging. SIAM Journal on Imaging Sciences, 9(1), 386-411. doi: 10.1137/15M1030807.
Gutiérrez, C. (2016). Interior Hölder Estimates for Second Derivatives. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 193-209). doi: 10.1007/978-3-319-43374-5_8.
Gutiérrez, C. (2016). Uniformly Elliptic Equations in Nondivergence Form. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 41-54). doi: 10.1007/978-3-319-43374-5_2.
Gutiérrez, C. (2016). Generalized Solutions to Monge–Ampère Equations. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 1-39). doi: 10.1007/978-3-319-43374-5_1.
Gutiérrez, C. (2016). W 2, p Estimates for the Monge–Ampère Equation. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 123-151). doi: 10.1007/978-3-319-43374-5_6.
Gutiérrez, C. (2016). Convex Solutions of det D 2 u = 1 in ℝ n. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 77-89). doi: 10.1007/978-3-319-43374-5_4.
Gutiérrez, C. (2016). The Cross-Sections of Monge–Ampère. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 55-76). doi: 10.1007/978-3-319-43374-5_3.
Gutiérrez, C. (2016). Regularity Theory for the Monge–Ampère Equation. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 91-122). doi: 10.1007/978-3-319-43374-5_5.
Gutiérrez, C. (2016). The Linearized Monge–Ampère Equation. In Progress in Nonlinear Differential Equations and Their Application, 89 (pp. 153-192). doi: 10.1007/978-3-319-43374-5_7.