A Struwe-type Decomposition Result for Weighted Critical $p$-Laplace Equations

TL;DR

This paper proves a decomposition theorem for Palais-Smale sequences related to weighted critical p-Laplace equations, revealing new rescaling laws due to weights in a bounded domain.

Contribution

It extends Struwe-type decomposition results to weighted critical p-Laplace equations, addressing challenges posed by weights and establishing new rescaling laws.

Findings

Established Struwe-type decompositions for weighted critical p-Laplace equations.

Identified key differences caused by weights in the equations.

Developed new rescaling laws to handle the weighted framework.

Abstract

We establish Struwe-type decompositions of Palais-Smale sequences for a class of critical $p$-Laplace equations of the Caffarelli-Kohn-Nirenberg type in a bounded domain $\Omega\subset\mathbb{R}^n$, $n\ge2$, containing the origin. In doing so, we highlight important differences introduced by the weights and require new rescaling laws to account for this new framework.