Calculus of Variations and Geometric Measure Theory
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M. G. Mora - L. Rondi - L. Scardia

The equilibrium measure for a nonlocal dislocation energy

created by mora on 04 Dec 2016

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Submitted Paper

Inserted: 4 dec 2016
Last Updated: 4 dec 2016

Year: 2016

Abstract:

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


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