$\overline\partial$-Equation on a Lunar Domain with Mixed Boundary Conditions

TL;DR

This paper investigates $L^2$-estimates for the $ar{ ext{d}}$-equation on lunar manifolds with mixed boundary conditions, extending existing methods to this specific geometric setting.

Contribution

It introduces a new application of Catlin and Catlin-Cho's methods to lunar domains with mixed boundary conditions for the $ar{ ext{d}}$-equation.

Findings

Established $L^2$-estimates for the $ar{ ext{d}}$-equation on lunar manifolds.

Extended the method of Catlin and Catlin-Cho to new geometric contexts.

Provided a framework for solving boundary value problems on lunar domains.

Abstract

In this paper, making use of the method developed by Catlin and Catlin-Cho,we study the $L^2$-estimate for the mixed boundary conditions on a lunar manifold with the mixed boundary conditions.