Lavrentiev Phenomenon in Nonlinear Elasticity

Abstract: In the calculus of variations, Lavrentiev's phenomenon refers to the situation when the minimum value of a certain functional varies significantly depending on the space of functions considered. In this talk, we present a new example of Lavrentiev's phenomenon in the context of nonlinear elasticity. This example is based on an interplay of the elastic energy’s resistance to infinite compression and the Ciarlet–Necas condition, a constraint preventing global interpenetration of matter on sets of full measure.

Mathematics

Audience: researchers in the topic

Trends in Mathematical Research