Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

M. G. Mora - L. Rondi - L. Scardia

The equilibrium measure for a nonlocal dislocation energy

created by mora on 04 Dec 2016


Submitted Paper

Inserted: 4 dec 2016
Last Updated: 4 dec 2016

Year: 2016


The aim of this paper is to characterise the equilibrium measure for a nonlocal and anisotropic weighted energy describing the interaction of positive dislocations in the plane. We prove that the minimum value of the energy is attained by a measure supported on the vertical axis and distributed according to the semi-circle law, a well-known measure which also arises as the minimiser of purely logarithmic interactions in one dimension. This result gives a positive answer to the conjecture that positive dislocations tend to form vertical walls.

Keywords: edge dislocations, nonlocal interaction, semi-circle law


Credits | Cookie policy | HTML 4.0.1 strict | CSS 2.1