A new example for the Lavrentiev phenomenon in Nonlinear Elasticity

TL;DR

This paper introduces a novel example demonstrating the Lavrentiev phenomenon in nonlinear elasticity, highlighting the complex interplay between elastic energy resistance and the Ciarlet-Nečas condition that prevents matter interpenetration.

Contribution

It provides the first explicit example of the Lavrentiev phenomenon in nonlinear elasticity involving the Ciarlet-Nečas condition.

Findings

Demonstrates the occurrence of the Lavrentiev phenomenon in a new elasticity context

Shows the impact of the Ciarlet-Nečas condition on energy minimization

Highlights the interplay between physical constraints and mathematical phenomena

Abstract

We present a new example for the Lavrentiev phenomenon in context of nonlinear elasticity, caused by an interplay of the elastic energy's resistance to infinite compression and the Ciarlet-Ne\v{c}as condition, a constraint preventing global interpenetration of matter on sets of full measure.