Global compactness for critical p-Laplacian Palais–Smale sequences in higher dimensions

Prove a Struwe-type bubble-profile decomposition and characterize the loss of compactness for possibly sign-changing Palais–Smale sequences associated with critical p-Laplacian Brezis–Nirenberg problems in dimensions N≥3 when p≠2.

Background

The paper establishes in the plane, for 1<p<2, a global compactness theorem for Palais–Smale sequences associated with critical p-Laplacian problems. The decomposition expresses loss of compactness through finite-energy entire solutions, while the nonexistence of finite-energy half-plane solutions excludes boundary bubbles.

The abstract states that the corresponding bubble-profile decomposition remains unresolved in dimensions N≥3 for p≠2. This is a higher-dimensional extension of Struwe’s global compactness result for the classical p=2 case.