Large $|k|$ behavior of d-bar problems for domains with a smooth boundary

TL;DR

This paper extends the analysis of large |k| behavior of d-bar problems from convex sets with real-analytic boundaries to those with smooth boundaries, utilizing almost holomorphic functions for the extension.

Contribution

It introduces a method to analyze d-bar problems for domains with smooth boundaries, broadening previous results limited to real-analytic boundaries.

Findings

Extended large |k| behavior analysis to smooth boundary domains

Utilized almost holomorphic functions for the extension

Provided new techniques for complex geometric optics solutions

Abstract

In a previous work on the large $|k|$ behavior of complex geometric optics solutions to a system of d-bar equations, we treated in detail the situation when a certain potential is the characteristic function of a strictly convex set with real-analytic boundary. We here extend the results to the case of sets with smooth boundary, by using almost holomorphic functions.