Harmonic analysis for elliptic partial differential equations. This project aims to establish fundamental estimates for elliptic partial differential equations, a crucial step in unravelling the behav

Description

Harmonic analysis for elliptic partial differential equations. This project aims to establish fundamental estimates for elliptic partial differential equations, a crucial step in unravelling the behaviour of solutions in real-world applications. The overall goal is to study the changes in these estimates as the equation coefficients, indicative of factors like the roughness of the medium, become increasingly singular, through investigating a longstanding conjecture of Pucci from 1966. Anticipated outcomes encompass the invention of a new class of fully nonlinear elliptic equations, along with new harmonic analysis techniques for studying them. The results will be a significant milestone for partial differential equations and solidify Australia's leadership in this cornerstone of modern mathematics.. Scheme: Discovery Projects. Field: 4904 - Pure Mathematics. Lead: A/Prof Po-Lam Yung