Weak compactness of solutions for fourth order elliptic systems with critical growth

TL;DR

This paper investigates the weak compactness of solutions to certain fourth order elliptic systems with critical growth, showing that weak limits of solutions are also solutions to a limit system, relevant for biharmonic mappings.

Contribution

It establishes weak compactness results for solutions of fourth order elliptic systems with critical growth, including systems related to biharmonic mappings in four dimensions.

Findings

Weak limits of solutions are solutions to the limit system.

The results apply to systems including biharmonic mappings.

Provides a foundation for analyzing stability of solutions.

Abstract

We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that weak limit of weak solutions to such systems is again a weak solution to a limit system.