A weighted Adams' inequality in $\mathbb{R}^4$ and applications

TL;DR

This paper establishes a weighted Adams' inequality in four-dimensional space, improves it via concentration-compactness, and applies these results to elliptic equations with exponential growth at infinity.

Contribution

It introduces a new weighted Adams' inequality in -dimensional space, enhances it with a concentration-compactness principle, and applies these to elliptic equations with exponential growth.

Findings

Established a weighted Adams' inequality in D

Proved an improved inequality using concentration-compactness

Applied results to elliptic equations with exponential growth

Abstract

In this paper, we establish a weighted Adams' inequality in some appropriate weighted Sobolev space in $\mathbb{R}^4$. Then we give an improvement inequality by proving the concentration-compactness result. In the last part, we consider an application to elliptic equation involving new exponential growth at infinity in $\mathbb{R}^4$.