Adams-Moser-Trudinger inequality in the cartesian product of Sobolev spaces and its applications

TL;DR

This paper extends Moser-Trudinger and Adams-Moser-Trudinger inequalities to Cartesian products of Sobolev spaces, and applies these results to analyze Kirchhoff systems with exponential non-linearities.

Contribution

It introduces non-singular and singular versions of these inequalities in product Sobolev spaces and applies them to complex Kirchhoff equations with exponential growth.

Findings

Established new inequalities in product Sobolev spaces

Derived applications to Kirchhoff equations with exponential non-linearity

Extended classical inequalities to more general functional settings

Abstract

The main aim of this article is to study non-singular version of Moser-Trudinger and Adams-Moser-Trudinger inequalities and the singular version of Moser-Trudinger equality in the Cartesian product of Sobolev spaces. As an application of these inequalities, we study a system of Kirchhoff equations with exponential non-linearity of Choquard type.