Connor Mooney

Associate Professor and Chancellor's Fellow
Department of Mathematics, UC Irvine

Office: Rowland Hall 410C
Email: mooneycr "at" math.uci.edu
Research Interest: Partial Differential Equations

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CV:

[.pdf]

Papers:

Mooney, C. Bernstein theorems for nonlinear geometric PDEs. Comm. Pure. Appl. Anal., to appear. [.pdf]
Mooney, C.; Wang, Z.; Xin, J.; Yu, Y. Global well-posedness and convergence analysis of score-based generative models via sharp Lipschitz estimates. Preprint 2024, arXiv:2405.16104. [.pdf]
Book review for Regularity Theory for Elliptic PDE, by Fernandez-Real and Ros-Oton. Bull. Amer. Math. Soc. 61 (2024), 515-524. [.pdf]
Bechtel, S.; Mooney, C.; Veraar, M. Counterexamples to maximal regularity for operators in divergence form. Arch. Math. 123 (2024), 199-209. [.pdf]
Du, W.; Mooney, C.; Yang, Y.; Zhu, J. A half-space Bernstein theorem for anisotropic minimal graphs. Preprint 2023, arXiv:2312.07519. [.pdf]
Hirsch, J.; Mooney, C.; Tione, R. On the Lawson-Osserman conjecture. Preprint 2023, arXiv:2308.04997. [.pdf]
Mooney, C.; Rakshit, A. Sobolev regularity for optimal transport maps of non-convex planar domains. SIAM J. Math. Anal. 56 (2024), 4742-4758. [.pdf]
Mitake, H.; Mooney, C.; Tran, H.; Xin, J.; Yu, Y. Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows. Math. Ann., to appear. [.pdf]
Mooney, C.; Savin, O. Non C^1 solutions to the special Lagrangian equation. Duke Math. J., to appear. [.pdf]
Mooney, C.; Yang, Y. The anisotropic Bernstein problem. Invent. Math. 235 (2024), 211-232. [.pdf]
Bhattacharya, A.; Mooney, C.; Shankar, R. Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase. Amer. J. Math., to appear. [.pdf]
Mooney, C.; Rakshit, A. Singular structures in solutions to the Monge-Ampere equation with point masses. Math. Eng. 5 (2023), Paper No. 083, 11 pp. [.pdf]
Mooney, C. Homogeneous functions with nowhere vanishing Hessian determinant. Ann. Inst. H. Poincare C Anal. Non Lineaire 41 (2024), 555-564. [.pdf]
Mooney, C. Hilbert's 19th problem revisited. Boll. Unione Mat. Ital. 15 (2022), 483-501. [.pdf]
Mooney, C.; Yang, Y. A proof by foliation that Lawson's cones are A_{Phi}-minimizing. Discrete Contin. Dyn. Syst. 41 (2021), 5291-5302. [.pdf]
Mooney, C. Solutions to the Monge-Ampere equation with polyhedral and Y-shaped singularities. J. Geom. Anal. 31 (2021), 9509-9526. [.pdf]
Mooney, C. Strict 2-convexity of convex solutions to the quadratic Hessian equation. Proc. Amer. Math. Soc. 149 (2021), 2473-2477. [.pdf]
Mooney, C. Entire solutions to equations of minimal surface type in six dimensions. J. Eur. Math. Soc. (JEMS) 24 (2022), 4353-4361. [.pdf]
Mooney, C. Singularities of complex-valued solutions to linear parabolic equations. Int. Math. Res. Not. IMRN 21 (2021), 4413-4426. [.pdf]
Mooney, C. Minimizers of convex functionals with small degeneracy set. Calc. Var. Partial Differential Equations 59 (2020), Paper No. 74, 1-19. [.pdf]
Ivanisvili, P.; Mooney, C. Sharpening the triangle inequality: envelopes between L^2 and L^p spaces. Anal. PDE 13 (2020), 1591-1603. [.pdf]
Mooney, C. A proof of the Krylov-Safonov theorem without localization. Comm. Partial Differential Equations 44 (2019), 681-690. [.pdf]
Mooney, C.; Savin, O. Regularity results for the equation u_{11}u_{22}=1. Discrete Contin. Dyn. Syst. 39 (2019), 6865-6876. [.pdf]
Mooney, C. The Monge-Ampere equation. Rend. Semin. Mat. Univ. Politec. Torino 76 (2018), 93-113. [.pdf]
Figalli, A.; Mooney, C. An obstacle problem for conical deformations of thin elastic sheets. Arch. Ration. Mech. Anal. 228 (2018), 401-429. [.pdf]
Mooney, C. Singularities in the calculus of variations. In Contemporary Research in Elliptic PDEs and Related Topics (Ed. Serena Dipierro), Springer INdAM Series 33 (2019), 457-480. [.pdf]
Collins, Tristan C.; Mooney, C. Dimension of the minimum set for the real and complex Monge-Ampere equations in critical Sobolev spaces. Anal. PDE 10 (2017), 2031-2041. [.pdf]
Mooney, C. Finite time blowup for parabolic systems in two dimensions. Arch. Ration. Mech. Anal. 223 (2017), 1039-1055. [.pdf]
Mooney, C. Some remarks on "Finite time blowup." (We improve the target dimension of the quasilinear example to m = 3). [.pdf]
Figalli, A.; Maggi, F.; Mooney, C. The sharp quantitative Euclidean concentration inequality. Camb. J. Math. 6 (2018), 59-87. [.pdf]
Mooney, C. Some counterexamples to Sobolev regularity for degenerate Monge-Ampere equations. Anal. PDE 9 (2016), 881-891. [.pdf]
Figalli, A.; Jhaveri, Y.; Mooney, C. Nonlinear bounds in Holder spaces for the Monge-Ampere equation. J. Funct. Anal. 270 (2016), 3808-3827. [.pdf]
Mooney, C.; Savin, O. Some singular minimizers in low dimensions in the calculus of variations. Arch. Ration. Mech. Anal. 221 (2016), 1-22. [.pdf]
Mooney, C. Harnack inequality for degenerate and singular elliptic equations with unbounded drift. J. Differential Equations 258 (2015), 1577-1591. [.pdf]
Mooney, C. W^{2,1} estimate for singular solutions to the Monge-Ampere equation. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), 1283-1303. [.pdf]
Mooney, C. Partial regularity for singular solutions to the Monge-Ampere equation. Comm. Pure Appl. Math. 68 (2015), 1066-1084. [.pdf]
Mooney, C. PhD Thesis. [.pdf]
Mooney, C. Undergraduate Thesis. [.pdf]

Notes:

Parabolic PDE. Based on informal lecture series at ETH Zurich, 2017. [.pdf]
Basic elliptic PDE. [.pdf]
Monge-Ampere equation. [.pdf]
Minimal surfaces. [.pdf]
Calculus of variations. [.pdf]

Seminar:

Virtual Analysis and PDE Seminar (VAPS)