Relaxation for an optimal design problem with nonstandard growth

TL;DR

This paper explores measure representations for functionals in optimal design problems with nonstandard growth and perimeter penalties, including applications to string modeling.

Contribution

It introduces a measure representation approach for complex functionals under non-standard growth conditions in optimal design.

Findings

Established measure representation for specific functionals

Extended the framework to problems with perimeter penalization

Applied results to string modeling scenarios

Abstract

In this paper we investigate the possibility of obtaining a measure representation for function- als arising in the context of optimal design problems under non-standard growth conditions and perimeter penalization. Applications to modelling of strings are also provided.