On the conjecture about Morrey quasiconvexity in L^{\infty}

TL;DR

This paper investigates the relationship between weak and strong Morrey quasiconvexity in L^{ }∞, demonstrating that weak Morrey quasiconvexity does not necessarily imply strong Morrey quasiconvexity through theoretical analysis and an example.

Contribution

It clarifies the distinction between weak and strong Morrey quasiconvexity in L^{ }∞ and provides an example showing they are not equivalent.

Findings

Weak Morrey quasiconvexity does not imply strong Morrey quasiconvexity.

The paper establishes relations between the two notions.

An explicit example demonstrates the non-implication.

Abstract

We study the difference between weak Morrey quasiconvexity and strong Morrey quasiconvexity in L^{\infty}. We point out some relations as well as give one example to show that weak Morrey quasiconvexity cannot imply strong Morrey quasiconvexity.