Volume 26, 2020
|Number of page(s)||43|
|Published online||06 March 2020|
Regularity of the minimiser of one-dimensional interaction energies
Faculty of Mathematics and Physics, Kanazawa University,
* Corresponding author: firstname.lastname@example.org
Accepted: 9 July 2019
We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind of Fredholm type. Our setting covers applications to dislocation pile-ups, contact problems, fracture mechanics and random matrix theory. Our main result shows that both the minimisation problems and the related singular integral equations have the same unique solution, which provides new regularity results on the minimiser of the energy and new positivity results on the solutions to singular integral equations.
Mathematics Subject Classification: 74G40 / 45Bxx / 26A33
Key words: Interaction energy / energy minimisation / regularity of the minimiser / singular integral equation
© EDP Sciences, SMAI 2020
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