Line-tension limits for line singularities and application to the mixed-growth case

TL;DR

This paper investigates the limits of line singularities in dislocation models using variational methods, demonstrating that asymptotic behaviors are consistent across different regularizations and energy growth conditions.

Contribution

It introduces a unified approach to analyze dislocation energies with various regularizations and growth conditions, establishing the independence of asymptotics from specific energy choices.

Findings

Asymptotic behavior is consistent across different regularizations.

Unified framework for energies with subquadratic growth.

Gamma convergence results are robust to regularization methods.

Abstract

We study variational models for dislocations in three dimensions in the line-tension scaling. We present a unified approach which allows to treat energies with subquadratic growth at infinity and other regularizations of the singularity near the dislocation lines. We show that the asymptotics via Gamma convergence is independent of the specific choice of the energy and of the regularization procedure.