Ground States of a Two Phase Model with Cross and Self Attractive Interactions

DOI10.1137/15M1033976zbMath1352.49009arXiv1507.08446OpenAlexW1611043320MaRDI QIDQ2823009

Lucia De Luca, Marco Cicalese, Marcello Ponsiglione, Matteo Novaga

Publication date: 6 October 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.08446

zbMATH Keywords

minimizersvariational methodsground stateshape optimizationnonlocal interactionsCoulomb kernel

Mathematics Subject Classification ID

Variational methods for problems in mechanics (70G75) Methods involving semicontinuity and convergence; relaxation (49J45) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Optimization of shapes other than minimal surfaces (49Q10) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items (10)

On the ternary Ohta-Kawasaki free energy and its one-dimensional global minimizers ⋮ Sorting Phenomena in a Mathematical Model For Two Mutually Attracting/Repelling Species ⋮ The isoperimetric problem for nonlocal perimeters ⋮ Segregation and domain formation in non-local multi-species aggregation equations ⋮ Equilibria for an Aggregation Model with Two Species ⋮ Attractive Riesz potentials acting on hard spheres ⋮ Some remarks on segregation of \(k\) species in strongly competing systems ⋮ Optimal Distribution of Oppositely Charged Phases: Perfect Screening and Other Properties ⋮ Nonlocal Shape Optimization via Interactions of Attractive and Repulsive Potentials ⋮ Multiple patterns formation for an aggregation/diffusion predator-prey system

Cites Work

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• Traveling waves for the mass in mass model of granular chains
• A note on non lower semicontinuous perimeter functionals on partitions
• Two-species particle aggregation and stability of co-dimension one solutions
• Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
• Nonlocal quantitative isoperimetric inequalities
• On minimizers of interaction functionals with competing attractive and repulsive potentials
• Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization
• Handling congestion in crowd motion modeling
• Isoperimetry and stability properties of balls with respect to nonlocal energies
• A double bubble assembly as a new phase of a ternary inhibitory system
• Existence of ground states of nonlocal-interaction energies
• Existence of compactly supported global minimisers for the interaction energy
• Singular patterns for an aggregation model with a confining potential
• Multiscale modeling of pedestrian dynamics
• Optimal Distribution of Oppositely Charged Phases: Perfect Screening and Other Properties
• On an Isoperimetric Problem with a Competing Nonlocal Term I: The Planar Case
• Measure solutions for non-local interaction PDEs with two species
• Nonexistence of a Minimizer for Thomas-Fermi-Dirac-von Weizsäcker Model
• Local and Global Minimality Results for a Nonlocal Isoperimetric Problem on $\mathbb{R}^N$
• On global minimizers of repulsive–attractive power-law interaction energies
• Free energy minimizers for a two-species model with segregation and liquid vapour transition
• Nonlocal Shape Optimization via Interactions of Attractive and Repulsive Potentials
• Isoperimetric problem with a coulomb repulsive term
• Stability for the Brunn-Minkowski and Riesz Rearrangement Inequalities, with Applications to Gaussian Concentration and Finite Range Non-local Isoperimetry

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