Vector variational problem with knitting boundary conditions

TL;DR

This paper studies a variational problem with complex boundary conditions related to suturing in plastic surgery, proving the existence of minimizers and discussing optimality conditions.

Contribution

It introduces a novel variational framework with knitting boundary conditions and establishes existence and optimality conditions for minimizers.

Findings

Existence of minimizers proved.

Necessary optimality conditions derived.

Applicable to suturing process modeling.

Abstract

We consider a variational problem with a polyconvex integrand and nonstandard boundary conditions that can be treated as minimization of the stress energy during the suturing process in the plastic surgery. Ex- istence of minimizers is proved as well as necessary optimality conditions are discussed.