Speaker: Ilya Marchenko
University of Notre Dame
Will give a PhD Defense entitled:
Asymptotic Expansions at Infinity for Solutions of Some Nonlinear Geometric PDE in Exterior Domains
Abstract: We study asymptotic behaviors of solutions of a family of fully nonlinear elliptic equations in \mathbb R^n\setminus\bar B_1 and establish expansions at infinity up to arbitrary order. We then prove the existence of solutions with prescribed asymptotic behavior at infinity and an arbitrarily high order of approximation. We also prove a similar existence result for solutions of the minimal surface equation in \mathbb R^n\setminus\bar B_1 whose gradient vanishes at infinity.
Date: 04-02-2024
Time: 9:00 am
Location: 127 Hayes-Healy
Zoom Link: https://notredame.