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

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.
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Taxonomy
TopicsAnalytic and geometric function theory · Nonlinear Partial Differential Equations · Advanced Harmonic Analysis Research
