Extremal function for a sharp Moser-Trudinger type inequality on the upper half space

TL;DR

This paper establishes a new sharp Moser-Trudinger inequality in the upper half space and proves the existence of extremal functions under dynamic conditions, advancing the understanding of nonlinear PDEs and geometric analysis.

Contribution

It introduces a novel sharp Moser-Trudinger inequality in two dimensions and demonstrates the existence of extremal functions in a dynamic setting.

Findings

Established a new sharp Moser-Trudinger inequality in the upper half space.

Proved the existence of extremal functions under dynamic changes in the unit ball.

Contributed to the analysis of nonlinear PDEs and geometric inequalities.

Abstract

Sharp Moser-Trudinger type inequalities and their extremal functions play an important role in studying nonlinear PDEs and geometry. We establish a new sharp Moser-Trudinger type inequality in the upper half space in two dimensions and prove the existence of extremal functions for a sharp Moser-Trudinger type inequality under dynamic changes in the unit ball.