Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations: VIASM 2016

by Nam Le, Hiroyoshi Mitake, Hung V. Tran

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry.   Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton–Jacobi equations.  

Kindle Edition

Published June 14, 2017

About the author

Nam Le came to Australia from Vietnam with his parents, when he was less than a year old, as a boat refugee. He went to Melbourne Grammar School and the University of Melbourne, from where he graduated with a BA (Hons) and LLB (Hons). His Arts thesis supervisor was the Australian poet Chris Wallace-Crabbe. He worked as a corporate lawyer and was admitted to the Supreme Court of Victoria in 2003/2004.
However, he decided to turn to writing, and in 2004 attended the Iowa Writers' Workshop in the United States of America where he completed a Masters in Creative Writing. He became fiction editor at the Harvard Review. His first short story was published in Zoetrope in 2006. Nam Le also held fellowships at the Fine Arts Work Center in Provincetown in 2006, and at the Phillips Exeter Academy, in 2007.
In an interview on Australian ABC radio, he said he turned from law to writing due to his love of reading: "I loved reading, and if you asked me why I decided to become a writer, that's the answer right there, because I was a reader and I was just so enthralled and thrilled by the stuff that I'd read that I just thought; what could be better? How could you possibly better spend your time than trying to recreate that feeling for other people". In the same interview he said that his first writing was poetry.
He returned to Australia in 2008, but is moving to Great Britain to take up a writing fellowship at the University of East Anglia.
When asked about his source of inspiration, Nam Le said in 2008 that "I’d say I’m most inspired by my parents for the choices and sacrifices they’ve made. It still boggles me".