A maximum-principle approach to the minimisation of a nonlocal dislocation energy

DOI10.3934/mine.2020012OpenAlexW3005403200MaRDI QIDQ2128523

Joan Mateu, Joan Verdera, Maria Giovanna Mora, Lucia Scardia, Luca Rondi

Publication date: 22 April 2022

Published in: Mathematics in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mine.2020012

zbMATH Keywords

maximum principlepotential theoryKirchhoff ellipsesdislocationsnonlocal interaction

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX) Statistical mechanics, structure of matter (82-XX)

Related Items

Editorial: Variational models in elasticity, Explicit minimisers for anisotropic Coulomb energies in 3D, Energy minimisers of perturbed dislocation energies, Stability of Ellipsoids as the Energy Minimizers of Perturbed Coulomb Energies, Global minimizers of a large class of anisotropic attractive‐repulsive interaction energies in 2D, The equilibrium measure for an anisotropic nonlocal energy, Explicit minimizers of some non-local anisotropic energies: a short proof, Equilibrium measure for a nonlocal dislocation energy with physical confinement

Cites Work

• Unnamed Item
• Unnamed Item
• Regularity of local minimizers of the interaction energy via obstacle problems
• Dimensionality of local minimizers of the interaction energy
• Explicit equilibrium solutions for the aggregation equation with power-law potentials
• The maximum principle and biharmonic functions
• The ellipse law: Kirchhoff meets dislocations
• Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics
• Existence of ground states of nonlocal-interaction energies
• Swarm dynamics and equilibria for a nonlocal aggregation model
• The Equilibrium Measure for a Nonlocal Dislocation Energy
• Existence of ground states for aggregation-diffusion equations
• Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction