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

• ### Christian Klein

Université de Bourgogne Franche-Comté, Dijon, France
• ### Johannes Sjöstrand

Université de Bourgogne Franche-Comté, Dijon, France
• ### Nikola Stoilov

Université de Bourgogne Franche-Comté, Dijon, France

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## Abstract

In this work we study the large $|k|$ behavior of complex geometric optics solutions to a system of d-bar equations for a potential being the characteristic function of a strictly convex set with smooth boundary, by using almost holomorphic functions. This is an extension of our previous work where we consider sets with real-analytic boundary.