Numerical evidence towards a positive answer to Morrey's problem

TL;DR

This paper presents numerical experiments indicating that in the planar case, rank-one convexity may imply quasiconvexity, providing evidence towards a positive answer to Morrey's problem.

Contribution

It offers numerical evidence and a heuristic explanation supporting the conjecture that rank-one convexity implies quasiconvexity in the plane.

Findings

Numerical experiments suggest rank-one convexity implies quasiconvexity in the planar case.

Provides a heuristic explanation for the observed numerical evidence.

Supports the conjecture related to Morrey's problem.

Abstract

We report on numerical experiments suggesting that rank-one convexity imples quasiconvexity in the planar case. We give a simple heuristic explanation of our findings.