Yu YUAN (袁域) - University of Washington
Yu YUAN (袁域) Department of Mathematics, Box 354350 University of Washington Seattle, Washington 98195 Email: yuan@math.washington.edu Phone: 206-616-5676 Fax: 206-543-0397 Office: Padelford C-523.
Department of Mathematics | University of Washington
Yu YUAN. A constant rank theorem for special Lagrangian Equations, submitted (with W. J. Ogden). Quadratic Hessian equation, Surveys in Geometric Analysis 2023, 157--177, Science Press, Beijing, 2024. Regularity for the Monge-Ampere equation by doubling, Math. Z. 307 (2024), no. 2, Paper No. 34, 7 pp. (with R. Shankar).
For the special Lagrangian equation, this C2,α estimate can also be achieved via geometric measure theory; for the Monge–Amp`ere equation, earlier in the 1950s, Calabi reached C3 estimates by interpreting the cubic derivatives in terms of the curvature of the correspond-ing Hessian metric g = D2u.
Yu YUAN M583E Spring19, M 3:30Œ4:50PM PDL C401; W 2:30Œ3:50PM DEN210 M581A Autumn 19, MW 9Œ10:20AM Linear Theory: Solvability, a priori estimates, Schauder and Calderon-Zygmund estimates, and regularity Nonlinear Theory: De Giorgi Nash Moser theory for divergence equa-tions (eg. minimal surface equation), Krylov-Safonov theory for nondiver-
Yu Yuan University of Washington, Department of Mathematics Box 354350, Seattle, WA 98195, USA and IAS, Princeton, NJ 08540, USA Dedicated to Louis Nirenberg on his 85th birthday Abstract. We show that any global convex solution to the Sigma-2 equation must be quadratic. 1. Introduction. In this note, we show that any global convex solution in ...
MICAH WARREN AND YU YUAN. Department of Mathematics, University of Washington, Seattle, Washington, USA. We derive a Liouville type result for special Lagrangian equations with certain “convexity” and restricted linear growth assumptions on the solutions. Keywords Liouville type theorems; Special Lagrangian equations.
HESSIAN AND GRADIENT ESTIMATES FOR THREE DIMENSIONAL SPECIAL LAGRANGIAN EQUATIONS WITH LARGE PHASE. By MICAH WARREN and YU YUAN. Abstract. We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three.
Note that the almost convexity condition for solutions in Guan and Qiu ([6] (15)) and McGonagle et al. ([9], Theorem 1.1) is essential in both the respective arguments toward Hessian estimates for quadratic Hessian equations. The mean value inequality in …
RAVI SHANKAR and YU YUAN Abstract We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions. Two decades ago, this result was obtained in three dimensions, as a by-product of the work on special Lagrangian equations. Warren’s rare ...
Abstract. We derive a priori interior Hessian estimates for special Lagrangian equations when the potential is convex. When the phase is very large, we show that con-tinuous viscosity solutions are smooth in the interior of the domain. c 2008 Wiley Periodicals, Inc.